Dr YUEN, Man Wai    阮文威 博士
Assistant Professor
Department of Mathematics and Information Technology
Contact
ORCiD
0000-0002-5035-3555
Phone
(852) 2948 8973
Email
yuenmw@eduhk.hk
Address
10 Lo Ping Road, Tai Po, New Territories, Hong Kong
Website
https://pappl.eduhk.hk/rich/web/person.xhtml?pid=139145&name=YUEN, Man Wai
Scopus ID
35093581700
ResearcherID
B-1210-2008
Research Interests
Math: Partial Differential Equations, Symmetry Reduction, Blowup, Euler-Poisson Equations, Euler Equations with or without Coriolis Force, Camassa-Holm Equations, Navier-Stokes Equations, Magnetohydrodynamics (MHD), Integrable System, Analytical and Exact Solutions, Mathematical Methods in Fluids, Classical Cosmology
Math Education: Mathematics Teachers' Competency, STEM Education, Mathematics Curriculum, TPACK in Mathematical Modelling, Methodology of Mathematics
Teaching Interests

Dr Yuen has the experience for teaching the following courses in the Education University of Hong Kong:


1. MTH 1025 Geometry and Measurement

2. MTH 1098 Calculus

3. MTH 2016/5015 Elementary Number Theory

4. MTH 2030 Learning Teaching and Assessment in Primary Math

5. MTH 2050/5050 Recreational Math

6. MTH 2100/3100 Vectors and Geometry

7. MTH 2110 Essential Mathematics Concepts

(with Textbook: Wong R.S.Y. and Yuen M.W. (2016). Essential Concepts of Set Theory. Hong Kong: Hong Kong Educational Publishing Company, ISBN: 978-988-236-584-1)

8. MTH 2111 Development of Mathematical Ideas

9. MTH 3107 Multi-variable Calculus

10. MTH 3139 Linear Algebra

11. MTH 3143 Differential Equations and Dynamical Modeling

12. GEJ 4020 Consolidating Undergraduate Learning through University ePortfolio

13. MTH 4105 Probability

14. MTH 4146 Numerical Methods

15. MTH 4900 Honor Projects II

16. FEX 5070/5077/5086/5129/5131/5133 Field Experience I/II

17. MTH 5186 Solving Real-life Problems with Modelling Techniques


External Appointments

1. An editorial member in

(a) the International Journal of Numerical Methods and Applications (ISSN: 0975-0452), indexed by Zentralblatt MATH and Excellence in Research for Australia (ERA), since 2013.

(b) the International Journal of Partial Differential Equations and Applications, Science and Education Publishing, indexed by Google Scholar, since 2013.

(c) the International Journal of Applied & Experimental Mathematics, since 2016.

(d) mathematical analysis of the Scientific World Journal (ISSN: 1537-744X), Hindawi Publishing Corporation, 2013-16.

2. An Co-editor for the Special Issue "Calculus and Symmetry/Asymmetry: Review paper" in Symmetry (Impact Factor 2020: 2.713, Raned ranked 33/73 in Multidisplinary Sciences) (co-editing with Prof. Svetlin G. Georgiev, Sorbonne University), with a deadline for manuscript submissions: 31 March 2022.

https://www.mdpi.com/journal/symmetry/special_issues/Calculus_Symmetry_Asymmetry_review_paper

3. A technical program committee member of international Conference on Partial Differential Equations (ICPDE) 2015-17.
1st conference Jul. 19-21, 2015, Shanghai, China; 2nd conference Jul. 25-27, 2016, Suzhou, China; The 3rd conference July 21-23, 2017, Jeju Island, South Korea (Organized by Scientific Research Publishing Inc.)

4. A committee member of the Hong Kong Mathematics Olympiad since 2012.

5. A committee member of moderation group for construction of mathematics test of Pre-S1 Hong Kong attachment test 2016-17.

6. An academic advisor to the Po Leung Kuk Primary Mathematics World Contest 2012-17.

Personal Profile

Dr. YUEN Manwai (Manwai YUEN) has been an assistant professor since 2014 in the Department of Mathematics and Information Technology at the Education University of Hong Kong (The Hong Kong Institute of Education), and as a lecturer in 2011-14. Dr. Yuen obtained a BSc (1st Hons) in computing math in 2003 and a MPhil in math in 2006 from the City University of Hong Kong; a MSc in math in 2004 and a PGDE in math education in 2007 from the Chinese University of Hong Kong; and a Ph.D. in applied math from the Hong Kong Polytechnics University in 2012, under the supervision of Prof. Kwong Man Kam, an ISI most highly cited mathematician 2001.

Dr. Yuen has been a Hong Kong registered teacher since 2007. From 2003-07 he was a part-time instructor, teaching Project Yijin math in Caritas Institute of Further and Adult Education in Kowloon; a full-time lecturer of math and statistics courses in the Hang Seng School of Commerce from 2007-08; and a tutor of undergraduate math courses in the City University of Hong Kong from 2004-06 and the Hong Kong Polytechnics University from 2008-09. Dr Yuen had been the field experience coordinator (Math) in 2014-21. Dr Yuen has been the programs leader in the Certificates in Professonal Develoment Programs in Emerging Technologies (E-Learning) in Primary and Secondary Chinese since 2016.

Dr. Yuen's research interest is applied analysis of nonlinear partial differential equations, specially involving blowup phenomena and similar solutions. Dr. Yuen's 80 journal papers (with 70 SCI or SSCI) were published by 40 international Math and Physics journals, including Journal of Mathematical Analysis and Applications, Communications in Nonlinear Science and Numerical Simulation, Journal of Mathematical Physics, Applied Mathematics Letters, Nonlinear Analysis and Studies in Applied Mathematics. His published papers have accumulated 689 citations and a H-index 15 from Scopus.


Meanwhile, he has also published 2 academic books. He is also a senior editor of the International Journal of Numerical Methods and Applications and an editorial board member in the International Journal of Partial Differential Equations and Applications and the International Journal of Applied & Experimental Mathematics.




Scopus: http://www.scopus.com/authid/detail.url?authorId=35093581700

EdUHK Repository: https://repository.eduhk.hk/en/persons/man-wai%E9%98%AE%E6%96%87%E5%A8%81-yuen

Researcher ID: http://www.researcherid.com/rid/B-1210-2008

ORCID: http://orcid.org/0000-0002-5035-3555

MathSciNet: http://www.ams.org/mathscinet/search/publications.html?pg1=INDI&s1=806774

Zentralblatt MATH: http://zbmath.org/authors/?s=0&c=100&q=yuen+manwai

ResearchGate: http://www.researchgate.net/profile/Manwai_Yuen

Research Interests
Math: Partial Differential Equations, Symmetry Reduction, Blowup, Euler-Poisson Equations, Euler Equations with or without Coriolis Force, Camassa-Holm Equations, Navier-Stokes Equations, Magnetohydrodynamics (MHD), Integrable System, Analytical and Exact Solutions, Mathematical Methods in Fluids, Classical Cosmology
Math Education: Mathematics Teachers' Competency, STEM Education, Mathematics Curriculum, TPACK in Mathematical Modelling, Methodology of Mathematics
Teaching Interests

Dr Yuen has the experience for teaching the following courses in the Education University of Hong Kong:


1. MTH 1025 Geometry and Measurement

2. MTH 1098 Calculus

3. MTH 2016/5015 Elementary Number Theory

4. MTH 2030 Learning Teaching and Assessment in Primary Math

5. MTH 2050/5050 Recreational Math

6. MTH 2100/3100 Vectors and Geometry

7. MTH 2110 Essential Mathematics Concepts

(with Textbook: Wong R.S.Y. and Yuen M.W. (2016). Essential Concepts of Set Theory. Hong Kong: Hong Kong Educational Publishing Company, ISBN: 978-988-236-584-1)

8. MTH 2111 Development of Mathematical Ideas

9. MTH 3107 Multi-variable Calculus

10. MTH 3139 Linear Algebra

11. MTH 3143 Differential Equations and Dynamical Modeling

12. GEJ 4020 Consolidating Undergraduate Learning through University ePortfolio

13. MTH 4105 Probability

14. MTH 4146 Numerical Methods

15. MTH 4900 Honor Projects II

16. FEX 5070/5077/5086/5129/5131/5133 Field Experience I/II

17. MTH 5186 Solving Real-life Problems with Modelling Techniques


External Appointments

1. An editorial member in

(a) the International Journal of Numerical Methods and Applications (ISSN: 0975-0452), indexed by Zentralblatt MATH and Excellence in Research for Australia (ERA), since 2013.

(b) the International Journal of Partial Differential Equations and Applications, Science and Education Publishing, indexed by Google Scholar, since 2013.

(c) the International Journal of Applied & Experimental Mathematics, since 2016.

(d) mathematical analysis of the Scientific World Journal (ISSN: 1537-744X), Hindawi Publishing Corporation, 2013-16.

2. An Co-editor for the Special Issue "Calculus and Symmetry/Asymmetry: Review paper" in Symmetry (Impact Factor 2020: 2.713, Raned ranked 33/73 in Multidisplinary Sciences) (co-editing with Prof. Svetlin G. Georgiev, Sorbonne University), with a deadline for manuscript submissions: 31 March 2022.

https://www.mdpi.com/journal/symmetry/special_issues/Calculus_Symmetry_Asymmetry_review_paper

3. A technical program committee member of international Conference on Partial Differential Equations (ICPDE) 2015-17.
1st conference Jul. 19-21, 2015, Shanghai, China; 2nd conference Jul. 25-27, 2016, Suzhou, China; The 3rd conference July 21-23, 2017, Jeju Island, South Korea (Organized by Scientific Research Publishing Inc.)

4. A committee member of the Hong Kong Mathematics Olympiad since 2012.

5. A committee member of moderation group for construction of mathematics test of Pre-S1 Hong Kong attachment test 2016-17.

6. An academic advisor to the Po Leung Kuk Primary Mathematics World Contest 2012-17.

Research Outputs
Scholarly Books, Monographs and Chapters
Wong R.S.Y. and Yuen M.W. (2016). Essential Concepts of Set Theory. Hong Kong: Hong Kong Educational Publishing Company, ISBN: 978-988-236-584-1..
Yuen, M.W. (2009). Some Problems on a Class of Fluid Dynamical Systems: Euler-Poisson, Navier-Stokes-Poisson, Euler and Navier-Stokes Equations. Saarbrücken: Verlag Dr. Müller, ISBN: 978-3-639-18357-3.

Journal Publications
Cheng, Q.Y., Fan E.G. and Yuen M.W. (2025). On the global well-posedness for the Fokas-Lenells equation on the line. J. Differential Equations 414 (2025), 34–93.. Journal of Differential Equations, 414, 34-93. https://doi.org/10.1016/j.jde.2024.09.008
An H.L., Hou, L.Y., Yuen M.W. (2024). The Extended Adomian Decomposition Method and its Application to the Rotating Shallow Water System for the Numerical Pulsrodon Solutions. Communications in Theoretical Physics, 76(12), 8 pp. https://doi.org/10.1088/1572-9494/ad674f
Cai, L., Lai N.A., Suen, A. and Yuen, M.W. (2024). Liouville-type Theorems for the Stationary Ideal Magnetohydrodynamics Equations in Rn. Journal of Mathematical Fluid Mechanics, 26, 13 pp. https://doi.org/10.1007/s00021-024-00902-2
Geng, J.B., Hu, K., Lai, N.A. and Yuen, M.W. (2024). Nonexistence of the Compressible Euler Equations with Space-dependent Damping in High Dimensions. Advances in Nonlinear Analysis, 13, 15 pp. https://doi.org/10.1515/anona-2024-0043
Fang, X.X., Ng, D.T.Z. and Yuen, M.W. (2024). Effects of Geogebra-enhanced Scratch Computational Thinking Instruction on Fifth-grade Students' Motivation, Anxiety, Cognitive load. Education and Information Technologies, In Press https://doi.org/10.1007/s10639-024-13052-9
SDGs infomation: 4 - Quality Education
Li X.L., Liu J.L. and Yuen M.W. (2024). Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in RN. Annals of Applied Mathematics, 40(3), 249-261. https://doi.org/10.4208/aam.OA-2024-0012
Dong, J.W. and Yuen, M.W. (2024). Remarks on Analytical Solutions to Compressible Navier-Stokes Equations with Free Boundaries. Advanced Nonlinear Studies, 24, 941–951. https://doi.org/10.1515/ans-2023-0146
He G.X., Yuen M.W. and Zhang, L.J. (2024). Exact spherically symmetric solutions of pressureless Navier-Stokes equations with density-dependent viscosity. Discrete and Continuous Dynamical Systems - Series S, In Press https://doi.org/10.3934/dcdss.2024115
Cheng H.F.K., Leung K.S., Leung K.C.I., Ma C.H., Man Y.K., Ng T.K.D. and Yuen M.W. (2024). Identifying Mathematics Teachers’ Competency to Look at Elementary Mathematics from an Advanced Standpoint: A Pilot Study. Frontiers in Education, 9, 12 pp. https://doi.org/10.3389/feduc.2024.1222510
SDGs infomation: 4 - Quality Education
Li, X.L., Liu, J.L. and Yuen M.W. (2024). Singularity Formation for the Relativistic Euler-Poisson Equations with Repulsive Force and Damping. Mathematical Methods in the Applied Sciences, 47, 6446-6456. https://doi.org/10.1002/mma.9930
Liu, J.L., Qin, Z.Y. and Yuen, M.W. (2024). Formation of Singularity for Isentropic Irrotational Compressible Euler Equations. Symmetry, 16 https://doi.org/10.3390/sym16040454
Qin, M.Y., Wang, Y.H. and Yuen, M.W. (2024). Optimal system, symmetry reductions and exact solutions of the (2 +1)-dimensional seventh-order Caudrey-Dodd-Gibbon-KP equation. Symmetry, 16 https://doi.org/10.3390/sym16040403
Fang, Y., Sang, X., Yuen, M.W. and Zhang, Y. (2024). N-dimensional Lattice Integrable Systems and their Bi-Hamiltonian Structure on the Time Scale using R-matrix Approach. Axioms, 13 https://doi.org/10.3390/axioms13030136
Fang, X.X, Ng, D.T.K., Tam W.T. and Yuen M.W. (2023). Integrating Computational Thinking into Primary Mathematics: A Case Study of Fraction Lessons with Scratch Programming Activities. Asian Journal for Mathematics Education, 2(2), 220-239. https://doi.org/10.1177/27527263231181963
Liu, X.T., Wen X.Y. and Yuen M.W. (2023). Cartesian Vector Solutions for N-dimensional Non-isentropic Euler Equations with Coriolis Force and Linear Damping. AIMS Mathematics, 8, 17171-17196. https://doi.org/10.3934/math.2023877
Yuen, M. W. (2023). Blowup for C1 Solutions of Euler Equations in R^N with the Second Inertia Functional of Reference. AIMS Mathematics, 8(4), 8162-8170. https://doi.org/10.3934/math.2023412
Geng, J.B., Lai, N.A., Yuen, M.W. and Zhou, J. (2023). Blow-up for Compressible Euler System with Space Dependent Damping in 1-D. Advances in Nonlinear Analysis, 12, 1-11. https://doi.org/10.1515/anona-2022-0304
Jiang, Z.W., Yuen, M.W. and Zhang, L.J. (2023). The Generalized Peakon Solution for the Rotation-two-component Camassa-Holm System. International Journal of Modern Physics B, 37, 2350017(12 Pages). https://doi.org/10.1142/S0217979223500170
Ng, D.T.K., Tsui. M.F. and Yuen M.W. (2022). Exploring the Use of 3D Printing in Mathematics Education: A Scoping Review. Asian Journal for Mathematics Education, 1, 338-358. https://doi.org/10.1177/27527263221129357
Liu, J.L., Wang, J.J. and Yuen, M.W. (2022). Blowup of Regular Solutions and C¹ Solutions for Free Boundary Problem of Euler–Poisson Equations with Repulsive Force in Rⁿ. Journal of Evolution Equations, 22, 14 Pages. https://doi.org/10.1007/s00028-022-00824-4
Wang, J.J., Wen X.Y. and Yuen, M.W. (2022). Blowup for Regular Solutions and C^1 Solutions of the Two-phase Model in R^N with a Free Boundary. AIMS Mathematics, 7(8), 15313-15330. https://doi.org/10.3934/math.2022839
Bai, H.W., Chow, K.W. and Yuen, M.W. (2022). Exact Solutions for the Shallow Water Equations in Two Spatial Dimensions: A Model for Finite Amplitude Rogue Waves. Partial Differential Equations in Applied Mathematics, 5, 1-5. https://doi.org/10.1016/j.padiff.2022.100360
Chen, Y., Wang, Y.H. and Yuen, M.W. (2022). Harmonic Solutions and Weak Solutions of Two-dimensional Rotational Incompressible Euler Equations. Partial Differential Equations in Applied Mathematics, 5, 1-4. https://doi.org/10.1016/j.padiff.2022.100336
Wang, J.D., Yuen, M.W. and Zhang, L.J. (2022). Persistence of Solitary Wave Solutions to a Singularly Perturbed Generalized mKdV Equation. Applied Mathematics Letters, 124, 107668.
Qin, M.L., Wen, X.Y. and Yuen, M.W. (2021). A Relativistic Toda Lattice Hierarchy, Discrete Generalized (m,2N−m)-Fold Darboux Transformation and Diverse Exact Solutions. Symmetry, 13(12), 1-27. https://doi.org/10.3390/sym13122315
Chen J. and Yuen M.W. (2021). Exact Solutions to the Three-dimensional Incompressible Magnetohydrodynamics Equations without Viscosity. Nonlinear Dynamics, 106, 919-926.
Fan, E.G. and Yuen, M.W. (2021). A Method for Constructing Special Solutions for Multidimensional Generalization of Euler Equations with Coriolis Force. Chinese Journal of Physics, 72, 134-144.
Liu, J.L., Wang, J.J. and Yuen, M.W. (2021). Blowup for C^1 Solutions of Compressible Euler Equations with Time-dependent Damping in R^n. Communications in Mathematical Sciences, 19, 513-528.
An, H.L., Fan, E.G. and Yuen, M.W. (2021). The N-dimensional Burgers Equation: A Bilinear Extension, Vortex, Fusion and Rational Solutions. Journal of Nonlinear Mathematical Physics, 28, 27-37.
Dong, J.J., Li, B. and Yuen, M.W. (2021). General High-order Breather Solutions, Lump Solutions and Mixed Solutions in the (2+1)-dimensional Bidirectional Sawada-Kotera Equation. Journal of Applied Analysis and Computation, 11, 271-286.
Dong, J.W. and Yuen, M.W. (2021). Some Special Self-similar Solutions for a Model of Inviscid Liquid-gas Two-phase Flow. Acta Mathematica Scientia, 41, 114-126.
Dong, J.W. and Yuen, M.W. (2020). Blowup of Smooth Solutions to the Compressible Euler Equations with Radial Symmetry on Bounded Domains. Zeitschrift für angewandte Mathematik und Physik, 71, Art. 189.
Ho, C.Y. and Yuen, M.W. (2020). Blowup for Projected 2-dimensional C^2 Solutions of Compressible Euler Equations with Coriolis Forces. Nonlinear Analysis: Real World Applications, 55, 103143.
Wong, S., Yeung, L.H. and Yuen, M.W. (2020). Exact solutions to 2D isothermal Euler-Poisson equations with qualitative analysis. Chinese Journal of Physics, 67, 293-304.
Tang, Y.N., Yuen, M.W. and Zhang, L.J. (2020). Double Wronskian Solutions to the (2+1)-dimensional Broer-Kaup-Kupershmidt Equation. Applied Mathematics Letters, 105, 106285.
Dong, J.J., Li, B. and Yuen, M.W. (2020). Soliton Molecules and Mixed Solutions of the (2+1)-dimensional Bidirectional Sawada-Kotera Equation. Communications in Theoretical Physics, 72, 025002.
Yuen, M.W. (2019). Blowup for Projected 2-Dimensional Rotational C^2 Solutions of Compressible Euler Equations. Journal of Mathematical Fluid Mechanics, 21, Art. 54.
Fan, E.G. and Yuen, M.W. (2019). Peakon Weak Solutions for the Rotation-two-component Camassa-Holm System. Applied Mathematics Letters, 97, 53-59.
Fan, E.G. and Yuen, M.W. (2019). Similarity Reductions and Exact Solutions for Two-dimensional Euler-Boussinesq Equations. Modern Physics Letters B, 33, 1950328.
An, H.L., Chan, W.H., Li, B. and Yuen, M.W. (2019). Analytical Solutions and Integrable Structure of the Time-dependent Harmonic Oscillator with Friction. Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, 74, 269-280.
An, H.L., Hou, L.Y. and Yuen, M.W. (2019). Analytical Cartesian Solutions of the Multi-component Camassa-Holm Equations. Journal of Nonlinear Mathematical Physics, 26, 255-272.
Cheung, K.L., Wong, S. and Yuen, M.W. (2018). Blowup Phenomenon for the Initial-boundary Value Problem of the Non-isentropic Compressible Euler Equations. Journal of Mathematical Physics, 59, 041502.
Yuen, M.W. (2018). Blowup for Regular Solutions and C^1 Solutions of Euler Equations in R^N with a Free Boundary. European Journal of Mechanics - B/Fluids, 67, 427-432.
Kwong, M.K. and Yuen, M.W. (2017). Pulsating Flows of the 2D Euler-Poisson Equations. Journal of Differential Equations, 263, 8508-8532.
Yuen, M.W. (2017). Blowup for Irrotational C^1 Solutions of the Compressible Euler Equations in R^N. Nonlinear Analysis-Theory Methods & Applications, 158, 132-141.
Yang, J. and Yuen, M.W. (2017). Cartesian Solutions for the Incompressible Density-dependent Euler-Poisson Equations in R^N. International Journal of Applied and Computational Mathematics, 3, 1549-1556.
Chen, Y., Fan, E.G. and Yuen, M.W. (2017). Explicitly Self-similar Solutions for the Euler/Navier-Stokes-Korteweg Equations in R^N. Applied Mathematics Letters, 67, 46-52.
Chow, K.W., Fan, E.G. and Yuen, M.W. (2017). The Analytical Solutions for the N-dimensional Damped Compressible Euler Equations. Studies in Applied Mathematics, 138, 294-316.
Yeung, L.H. and Yuen, M.W. (2017). Some Analytical Solutions for the Euler and Euler-Poisson Equations. Neural, Parallel, and Scientific Computations, 25, 37-44.
An, H.L., Kwong, M.K. and Yuen, M.W. (2017). Perturbational Self-similar Solutions of the Multi-dimensional Camassa-Holm-type Equations. Electronic Journal of Differential Equations, 2017 (48), 1-12.
An, H.L., Cheung, K.L. and Yuen, M.W. (2016). Perturbational Self-similar Solutions for the 2-component Degasperis-Procesi System via a Characteristic Method. Turkish Journal of Mathematics, 40, 1237-1245.
Kwong, M.K. and Yuen, M.W. (2016). New Method for Blowup of the Euler-Poisson System. Journal of Mathematical Physics, 57(8), 083501.
Chan, W.H., Wong, S. and Yuen, M.W. (2016). Blowup of Regular Solutions for the Relativistic Euler-Poisson Equations. Journal of Mathematical Analysis and Applications, 439, 925-936.
Chen, Y., Fan, E.G. and Yuen, M.W. (2016). The Hopf-Cole Transformation, Topological Solitons and Multiple Fusion Solutions for the N-dimensional Burgers System. Physics Letters A, 380, 9-14.
Wong, S. and Yuen, M.W. (2015). Blow-up Phenomena for Compressible Euler Equations with Non-vacuum Initial Data. Zeitschrift für angewandte Mathematik und Physik, 66, 2941-2955.
An, H.L., Yang, J.J. and Yuen, M.W. (2015). Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid. Communications in Theoretical Physics, 63, 613-618.
Yuen, M.W. (2015). Rotational and Self-similar Solutions for the Compressible Euler Equations in R^3. Communications in Nonlinear Science and Numerical Simulation, 20, 634-640.
An, H.L., Fan, E.G. and Yuen, M.W. (2015). The Cartesian Vector Solutions for the N-dimensional Compressible Euler Equations. Studies in Applied Mathematics, 134, 101-119.
Kwong, M.K. and Yuen, M.W. (2014). Periodic Solutions of 2D Isothermal Euler-Poisson Equations with Possible Applications to Spiral and Disk-like Galaxies. Journal of Mathematical Analysis and Applications, 420, 1854-1863.
Yuen, M.W. (2014). Blowup for C^2 Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology. Journal of Mathematical Analysis and Applications, 415, 972-978.
Yuen, M.W. (2014). Vortical and Self-similar Flows of 2D Compressible Euler Equations. Communications in Nonlinear Science and Numerical Simulation, 19, 2172-2180.
An, H.L. and Yuen, M.W. (2014). Drifting Solutions with Elliptic Symmetry for the Compressible Navier-Stokes Equations with Density-dependent Viscosity. Journal of Mathematical Physics, 55(5), 053506.
Wong, S. and Yuen, M.W. (2014). Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions (doi: 10.1155/2014/580871). The Scientific World Journal, Retrieved from http://dx.doi.org/10.1155/2014/580871, online publication, 1-5.
Fan, E.G. and Yuen, M.W. (2014). Similarity Reductions and New Nonlinear Exact Solutions for the 2D Incompressible Euler Equations. Physics Letters A, 378, 623-626.
Yuen, M.W. (2013). Stabilities for Euler-Poisson Equations with Repulsive Forces in R^N. International Journal of Mathematical Analysis, 7, 2787-2795.
An, H.L., Cheung, K.L. and Yuen, M.W. (2013). A Class of Blowup and Global Analytical Solutions of the Viscoelastic Burgers' Equations. Physics Letters A, 377, 2275-2279.
An, H.L. and Yuen, M.W. (2013). Supplement to "Self-similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^N" [Commun Nonlinear Sci Numer Simu. 17 (2012) 4524-4528]. Communications in Nonlinear Science and Numerical Simulation, 18, 1558-1561.
Yuen, M.W. (2013). Blowup for the Inviscid Proudman-Johnson Equation with the Homogeneous Three-point Boundary Condition. Applied Mathematical Sciences, 7, 2591-2597.
Yeung, L.H. and Yuen, M.W. (2013). Line Solutions for the Euler and Euler-Poisson Equations with the Multiple Gamma Law. Far East Journal of Mathematical Sciences, 72, 313-329.
Yuen, M.W. (2012). Self-similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^N. Communications in Nonlinear Science and Numerical Simulation, 17, 4524-4528.
Cheung, K.L. and Yuen, M.W. (2012). Some Exact Blowup or Global Solutions for the Non-isentropic Navier-Stokes Equations with Density-dependent Viscosity. Results in Physics, 2, 55-57.
Yuen, M.W. (2012). Perturbational Blowup Solutions to the 2-component Camassa–Holm Equations. Journal of Mathematical Analysis and Applications, 390, 596-602.
Yeung, L.H. and Yuen, M.W. (2012). Note for "Some Exact Blowup Solutions to the Pressureless Euler Equations in R^N" [Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 2993-2998]. Communications in Nonlinear Science and Numerical Simulation, 17, 485-487.
Yeung, L.H. and Yuen, M.W. (2011). Analytical Solutions to the Navier-Stokes-Poisson Equations with Density-dependent Viscosity and with Pressure. Proceedings of the American Mathematical Society, 139, 3951-3960.
Yuen, M.W. (2011). Blowup for the C¹ Solutions of the Euler-Poisson Equations of Gaseous Stars in R^N. Journal of Mathematical Analysis and Applications, 383, 627-633.
Yuen, M.W. (2011). Perturbational Blowup Solutions to the compressible 1-dimensional Euler Equations. Physics Letters A, 375, 3821-3825.
Yuen, M.W. (2011). Self-similar Solutions to the 2-component Degasperis-Procesi Shallow Water System. Communications in Nonlinear Science and Numerical Simulation, 16, 3463-3469.
Yuen, M.W. (2011). Exact, Rotational, Infinite Energy, Blowup Solutions to the 3-dimensional Euler Equations. Physics Letters A, 375, 3107-3113.
Yuen, M.W. (2011). Some Exact Solutions to the Pressureless Euler Equations in R^N. Communications in Nonlinear Science and Numerical Simulation, 16, 2993-2998.
Yuen, M.W. (2011). Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars II. Journal of Mathematical Physics, 52, 073512.
Yuen, M.W. (2011). Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces. Nonlinear Analysis: Theory, Methods & Applications, 74, 1465-1470.
Yeung, L.H. and Yuen, M.W. (2010). Some Exact Blowup Solutions to Simple Cosmology Models. Applied Mathematical Sciences, 4, 3317-3326.
Yuen, M.W. (2010). Self-similar Blowup Solutions to the 2-component Camassa-Holm Equations. Jounral of Mathematical Physics, 51, 093524.
Yuen, M.W. (2009). Analytically Periodic Solutions to the Three-dimensional Euler-Poisson Equations of Gaseous Stars with a Negative Cosmological Constant. Classical and Quantum Gravity, 26, 235011.
Yuen, M.W. (2009). Analytical Blowup Solutions to the Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity in R^N. Nonlinearity, 22, 2261-2268.
Yeung, L.H. and Yuen, M.W. (2009). Analytical Solutions to Navier-Stokes Equations with Density-dependent Viscosity and with Pressure. Journal of Mathematical Physics, 50, 083101.
Yuen, M.W. (2008). Analytical Solutions to the Navier-Stokes Equations. Journal of Mathematical Physics, 49, 113102.
Yuen, M.W. (2008). Stabilities for Euler-Poisson Equations in Some Special Dimensions. Journal of Mathematical Analysis and Applications, 344, 145-156.
Yuen, M.W. (2008). Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars. Journal of Mathematical Analysis and Applications, 341, 445-456.
Yuen, M.W. (2007). Blowup Solutions for a Class of Fluid Dynamical Equations in R^N. Journal of Mathematical Analysis and Applications, 329, 1064-1079.

Conference Papers
Yuen, K.K.F. and Yuen, M.W. (2012, August). Department Course Selection Problem: The Primitive Cognitive Network Process Approach. Proceedings of IEEE International Conference on Teaching, Assessment, and Learning for Engineering, TALE 2012 , art. no. 6360327 , pp. H1C15-H1C17, Hong Kong.
Yuen, M.W. (2011, September). Cylindrical Solutions to the Isothermal Euler-Poisson Equations. Discrete and Continuous Dynamical Systems -- Supplement 2011, Dynamical Systems, Differential Equations and Applications 8th AIMS Conference, 1448-1456. ISBN-13: 978-1-60133-007-9, Springfield.

All Other Outputs
Yuen, M.W. (2014). Review of "On Steady Subsonic Flows for Euler-Poisson Models". MathSciNet, American Mathematical Society.
Yuen, M.W. (2013). Review of "Stationary Solutions of Euler-Poisson Equations for Non-isentropic Gaseous Stars". MathSciNet, American Mathematical Society..

Projects
Vanishing Viscosity Solutions to a Family of Active Vector Equations for Modelling Magnetic Relaxation
Active vector equations can be regarded as a special type of differential equations in which the unknown vector-valued function is related to the velocity field via some constitutive laws. This kind of differential equations comes from many physical models such as the in compressible Euler equations or magnetohydrodynamics (MHD), all of them have great importance in practical applications ranging from fluid mechanics to geophysics, astrophysics, cosmology and engineering.
The primary goal of this project is to achieve some fundamental results on a general class of viscous active vector equations in various regimes of parameters, which include the global in-time well-posedness and the convergence of solutions when the diffusive parameters vanish. Such proposed problem is fruitful in the sense that by establishing well-posedness under the smoothing effects on the magnetic and velocity vector fields, it provides approximate solutions for the related inviscid models that will help identify singular behaviours as those diffusive parameters vanish. The secondary goal of this project is to rigorously address a class of inviscid active vector equations arising from the viscous models that are just mentioned in the primary goal. Such problem is crucial but challenging because these inviscid models come from a topology preserving diffusion process known as magnetic relaxation, in which its physical and mathematical properties are not yet fully understood.
Project Start Year: 2025, Principal Investigator(s): SUEN, Chun Kit, Anthony (YUEN, Man Wai as Co-Investigator)

 
Croucher Chinese Visitorship Scholars 2024/25
The funding supports Prof. Lai Ningan, Zhejiang Normal University for the 6 months visit to Department of Mathematics and Information Technology, The Education University of Hong Kong. For research works in Hong Kong under this project, we aim to 1. Finite time blow blow-up for compressible Euler system (1) with “critical” space dependent damping in R^N; 2. Local well posedness for isothermal compressible Navier-Stokes system with large data.
Project Start Year: 2024, Principal Investigator(s): YUEN, Man Wai

 
Provision of Service for the "Development and Delivery of 18-hour Enrichment Courses for Teachers on Mathematical Modelling in Secondary Schools"
This project is to provide the service for the development and delivery of 18-hour enrichment courses for teachers on mathematical modelling in Hong Kong secondary schools in 2024-25.
Project Start Year: 2024, Principal Investigator(s): YUEN, Man Wai
SDGs Information: 4 - Quality Education
 
Provision of Services for the Pilot Scheme on Introducing Mathematical Modelling to the Primary Mathematics Curriculum
The project provides the services for the Pilot Scheme on Introducing Mathematical Modelling to the Primary Mathematics Curriculum from Feb 2024 to Dec 2025.
Project Start Year: 2024, Principal Investigator(s): YUEN, Man Wai

 
Provision of Services for the "Enhanced Programme on Promoting Mathematical Modelling for Teachers and Students in Secondary Schools"
For the promotion of STEAM Education, the Curriculum Development Institute of the Education Bureau commissioned the Education University of Hong Kong to organize the said courses, which aims at enriching teacher’s and student’s knowledge and skills in understanding mathematical modelling and its applications in 2024.
Project Start Year: 2024, Principal Investigator(s): YUEN, Man Wai

 
The Study on Ermakov Structure and related Problems in Some Important Nonlinear Wave Equations
Solutions of nonlinear wave equations are not only helpful for us to better understand the related physical phenomena, but also play an important role to promote new physical and engineering applications. Therefore, the study on solutions of nonlinear wave equations has been a hot topic in the world. In this project, we shall study Ermakov structures and related problems in some nonlinear wave equations with a multiplicative noise of advection type. The implementation of the project will provide a new tool to seek solutions of nonlinear wave equations. The results can have important theoretical meanings and practical values in the areas of nonlinear science and engineering technology.
Project Start Year: 2024, Principal Investigator(s): AN, Hongli (YUEN, Man Wai as Co-Investigator)

 
Provision of Service for the "Development and Delivery of 18-hour Enrichment Courses for Teachers on Mathematical Modelling in Secondary Schools"
This project is to provide the service for the development and delivery of 18-hour enrichment courses for teachers on mathematical modelling in Hong Kong secondary schools in 2023-24.
Project Start Year: 2023, Principal Investigator(s): YUEN, Man Wai

 
Quantitative Analysis of Modified Euler-Poisson System
The primary goal of this project is to achieve some basic but interesting results on the modified Euler Poisson system. Problems governed by the modified Euler-Poisson equations are difficult to be solved due to the existence of highly nonlinear momentum equations in the Euler equations. Thus, by providing concrete examples involving modified Euler-Poisson equations in real-life mathematical models, one can help scientists understand and validate the corresponding physical phenomena at a deeper level.
Project Start Year: 2023, Principal Investigator(s): YUEN, Man Wai

 
The Cauchy Problem for Isothermal Euler Equations
In this project, we will estimate the existence time of smooth solutions to isothermal compressible Euler equations. First, we shall prove that minimal existence time can be estimated if suitable initial data are chosen. Second, we will establish that maximal existence time can be determined if some initial functional conditions are satisfied.
Project Start Year: 2023, Principal Investigator(s): YUEN, Man Wai

 
Provision of Services for the "Enhanced Programme on Promoting Mathematical Modelling for Teachers and Students in Secondary Schools"
For the promotion of STEAM Education, the Curriculum Development Institute of the Education Bureau commissioned the Education University of Hong Kong to organize the said courses, which aims at enriching teacher’s and student’s knowledge and skills in understanding mathematical modelling and its applications in 2023.
Project Start Year: 2023, Principal Investigator(s): YUEN, Man Wai

 
The Solutions of the Three-dimensional Compressible Magnetohydrodynamics System
The aims of this research project are as follows: (a) Construct the stationary and non-stationary ABC flow with rotational blowup solutions with rational functions for the compressible MHD equations; (b) Present general exact solutions with nonlinear functions of the spatial variables for the two- and three-dimensional compressible MHD equations.
Project Start Year: 2022, Principal Investigator(s): YUEN, Man Wai

 
Croucher Foundation Visitorship for PRC Scholars 2022/23
The funding supports Dr Xi Shuai, Shandong University of Science and Technology for the 6 months visit to Department of Mathematics and Information Technology, The Education University of Hong Kong. For research works in Hong Kong under this project, we aim to
1. Global well-posedness of the mild solution to the two-dimensional incompressible MHD equations with Coriolis Force
2. Global well-posedness of the mild solution to incompressible nematic liquid crystal flow
Project Start Year: 2022, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Visual Proof of the Irrationality of Certain Numbers
Certain theorems in number theory or algebra may involve logical arguments that are not easily understood by high school students. Some work has been done in recent decades to prove such theorems without using any written statement, i.e. with only a self-explanatory diagram. One needs only a little hint to discover the proof from the diagram himself. The research aims to discover more such proofs of theorems, especially the more important ones like the irrationality of root 2. Then we can consider further extending the proof to other irrational numbers based on this method.
Project Start Year: 2021, Principal Investigator(s): YUEN, Man Wai 阮文威

 
The Evolution of the Solutions of the Non-isentropic Euler Equations
..
Project Start Year: 2020, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Croucher Foundation Visitorship for PRC Scholars 2020/21
The funding supports Dr Fang Yong, Shandong University of Science and Technology for the 6 months visit to Department of Mathematics and Information Technology, The Education University of Hong Kong. For research works in Hong Kong under this project, we aim to
1. To conduct applied analysis about the known results for Euler equations with Coriolis force.
2. To construct the Lie symmetry analysis of dynamical systems on a time scale.
3. To apply this new Lie symmetry analysis method to derive the symmetry with a single parameter group of the Euler equation with Coriolis force on a time scale.
Project Start Year: 2020, Principal Investigator(s): YUEN, Man Wai 阮文威

 
On New Analytical Solutions and Mathematical Properties for High Dimensional and Multi-component Camassa-Holm Systems
The classical Camassa-Holm (CH) equation is one of most fundamental water system, which models the unidirectional propagation of shallow water waves. In this project, we aim
1. To develop systemical methods to construct analytical and exact solutions for high dimensional and multi-component Camassa-Holm systems.
2. To perform theoretical analysis on the algebraic property, asymptotic property and stability of the analytical and exact solutions.
Project Start Year: 2020, Principal Investigator(s): YUEN, Man Wai 阮文威

 
FLASS Internationalization and Exchange Scheme
This funding is to support Prof. Qiao Zhijun, The University of Texas Rio Grande Valley, for 12 days visit in The Education University of Hong Kong. The major objective of this visit is to develop a new mathematical technique to examine in detail negative order hierarchy of dynamical systems and to characterize some members in the negative order hierarchy with peakon, cuspon, and weak kink solutions.
Project Start Year: 2020, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Tin Ka Ping Education Fund Visiting Scholars Exchange Programme 2019/20
This funding is to support Prof. Zhang Lijiun, Shangdong University of Science and Technology, for 7 days visit in The Education University of Hong Kong. During the visit, the singular solutions of shallow water wave equations will be considered by using phase portrait analysis, asymptotic analysis, bifurcation analysis and numerical method.
Project Start Year: 2019, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Exact Solutions of the Incompressible Magnetohydrodynamics System
The objectives of this research project are to: (a) construct the stationary and non stationary ABC flow, the rotational blowup solutions with rational functions for the MHD equations; (b) present general exact solutions with nonlinear functions of the spatial variables for the 2-dimensional and 3-dimensional MHD equations.
Project Start Year: 2019, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Identifying Mathematics Teachers’ Competency in Terms of Their Capacity on Looking at Elementary Mathematics from an Advanced Standpoint
We identify an additional knowledge domain which was originally defined by Felix Klein in the last century. The knowledge might serve as an added condition of sufficiency for effective teaching, delivered by Mathematics teachers – the capability of looking at elementary Mathematics from an advanced standpoint (EMFAS). In this study, we attempt to investigate and identify both fresh and pre-service teachers’ knowledge by applying the technique of EMFAS into their ability by analyzing mathematically the dimensional exchanges on solving some specifically constructed problems or justifying various propositions in a written test. The term dimensional exchanges refers to the situations where knowledge evolves during mathematical interpretation and justification between dimensions such as concrete-to-abstract, particular-to-general, local-to-global (properties), etc. This study is a continuation of a small project done by the one of the Co-I’s in 2016-17. Invited participants have to show details of derivations in their responses in a prescribed written test on some specially designed item questions on how to deliver Mathematics knowledge to students at the elementary level with respect to the advanced knowledge they possess. We shall explain why EMFAS would be a new knowledge domain beyond the traditional pedagogical content knowledge (PCK) and subject matter knowledge (SMK) between which the inter-relationship is not very apparent in the traditional construct of Mathematics knowledge domain (see for example Ball, et al 2005). The results may serve as an indicator to determine Mathematics teachers’ proficiency in applying the technique of EMFAS. It has been a general belief that both SMK and PCK are essential for effective teaching, and thus, under normal circumstance, leads to students’ effective learning. Proficiency of EMFAS provide a foundation to bridge SMK between advanced and elementary levels, This connection is not guaranteed during knowledge delivery by teachers who only possess sufficient PCK and SMK, but not proficiency of EMFAS. The previous study on this topic hinted a situation that EMFAS would be another additional knowledge domain in the component of Mathematics teachers’ professional competency. Unfortunately, there is no special training in this particular topic in the curriculum of Mathematics teacher education. We conclude it by suggesting a way out of the current situation in the curriculum of teacher education. It is our belief that subject knowledge guides pedagogy. While, capacity of looking at EMFAS is a very special type of subject knowledge that could play an important role in guiding pedagogy.
Project Start Year: 2019, Principal Investigator(s): YUEN, Man Wai 阮文威

 
The Flows of N-dimensional Burgers Equations
Burgers equations are a basic and important partial differential equation coming from fluid mechanics. In this project, based on our previous works, we develop and apply different approaches and techniques to discover more general Hopf-Cole transformation, the novel similarity transformation and similarity solutions, Lie symmetry group and group invariant solution, analytical solutions for the n-dimensional Burgers equations.
Project Start Year: 2019, Principal Investigator(s): YUEN, Man Wai 阮文威

 
The Life Span of the Solution for the Euler-Poisson Equations
This is the plot study for GRF appliction for the life span of the solution for the Euler-Poisson equations.
Project Start Year: 2018, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Croucher Foundation Visitorship for PRC Scholars 2018/19
The funding supports Dr Wang Yunhu, Shanghai Maritime Univerisity for the 6 months visit to Department of Mathematics and Information Technology, The Education University of Hong Kong. For research works in Hong Kong under this project, we aim to (i) give the exact solutions for 2D and 3D Euler/Navier–Stokes–Korteweg equations; and (ii) investigate the integrabilities for 2D and 3D Euler/Navier–Stokes–Korteweg equations, including Lax pairs and Bäcklund transformation and then further to find the soliton solutions and even interaction solutions among different nonlinear activation.
Project Start Year: 2018, Principal Investigator(s): YUEN, Man Wai 阮文威

 
The Flows of the Euler Equations with Coriolis Force in Ocean Dynamics
The Euler equations with Coriolis force which is a natural force caused by the rotation of the earth, form the classical model in oceanography and atmospheric dynamics. The Euler equations can provide good approximations and predictions for the real world applications in ocean dynamics. Many scientists and mathematicians have focused on the studies of the exact solutions and qualitative properties of the flow of the Euler equations in fluid dynamics. However, due to the difficulty for controlling the additional term, the rotational force, it is hard to obtaining the corresponding results for the exact solutions and the qualitative study of the Euler equations with Coriolis force, comparing with the classical Euler equations without rotational forces, based on the P.I.’s knowledge.
This proposal concerns new exact solutions and the qualitative studies on the flows of the Euler equations with Coriolis force, we aim to develop new methods about the exact solutions and the qualitative properties of the flows for better understanding the nonlinear behavior of the Euler equations with Coriolis force.
Project Start Year: 2018, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Blowup for Non-Vacuum Solutions of Euler Equations in R^N
The blowup mechanism in the N-dimensional compressible Euler equations in fluid mechanics arouses the keen investigation of scientists and mathematicians as it is highly related the incompressible Navier-Stokes equations, one of the Clay Institute millennium prize problems. In this project, we want to investigate the new blowup phenomena for the solutions of the Euler equations with initial non-vacuum conditions. The energy methods, functional methods and constructing exact solutions for the compressible Euler equations will be restudied for the improving the blowup set.
Project Start Year: 2017, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Analytical Solutions for the Camassa-Holm System in R^N
In this project, we focus on two aspects of two-component Camassa-Holm (CH) equations, multi-component CH equations, high dimensional CH equations and rotation-two-component CH equations:
1. The exact solution of physical interests: We aim to search new methods to construct three kinds of exact solutions, including general Cartesian solutions, self-similar solutions, peakon solutions for two-component CH equations, multi-component CH equations, high dimensional CH equations and rotation-two-component CH equations.
2. The classification of travelling wave solutions: We should give travelling wave classification for two-component CH equations, multi-component CH equations, high dimensional CH equations and rotation-two-component CH equations.
Project Start Year: 2017, Principal Investigator(s): YUEN, Man Wai 阮文威

 
New Methods for Blowup Properties of the Euler-Poisson Equations with Free Boundaries
A lot of scientists and mathematicians have focused on the studies of the singularity formation in fluid dynamics as the problems have are the physical significance with hard challenge. In this proposed project, we will study about the long-time behavior of the solution of the Euler-Poisson equations, including the blowup phenomena and the global existence. Based on three known approaches, the integration method, the differentiation method and the energy method, in this proposed study, we aim to develop new methods for answering if the new blowup phenomena exist for the Euler-Poisson equations with free boundaries. We accredit that the new methods and results will be valuable for the science community and our perceptiveness of the Euler-Poisson equations. In addition, the new developed methods in this project, can contribute more tools for the scientists and mathematicians to investigate the blowup phenomena and the global existence of the related and similar nonlinear partial differential equations in classical fluid dynamics, astrophysics, semiconductor physics.
Project Start Year: 2017, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Blowup Phenomena for the Euler-Poisson Equations with Damping
The appearance of singularity in the solutions of mathematical models in fluid dynamics has long been a matter of concern for physicists and mathematicians alike. In this project, we are going to explore the long time behaviour of the Euler-Poisson equations with damping, which the phenomena of finite-time singularity or global existence of the solutions will be studied. We have many ways to tackle the problem, including integration method, differentiation method, functional methods, constructing exact solutions and ad hoc methods. Our aim is to obtain results which will lead to one publication on blowup or global existences of the compressible Euler-Poisson equations with damping and to develop new methods for proving blowup or showing the global existences. The discovery of these methods will provide useful tools for the study of blowup and the global existences of the Euler-Poisson equations with damping, and may even be extendable to nonlinear evolution systems, for example, the compressible Euler equations and the Euler-Poisson equations without damping. In addition, we want to see the differences between the systems with and without damping. Our results will have useful physical applications as well as providing new insights into the Euler-Poisson equations with damping and related systems.
Project Start Year: 2016, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Exact Analytic Solutions and Dynamical Behaviors for the Viscous Primitive Equations of Geophysics
The viscous primitive equations of geophysics are important mathematical models in viscous incompressible fluid, geophysics, atmospheric dynamics etc. In this proposed project, we are interested in constructing the novel analytical exact solutions via effective approaches, including Clarkson-Kruskal method, curve integration method et al. Mathematical and physical properties of the solutions such as blowup phenomenon, stability, dynamical behaviors et al will be further analyzed. The investigations in this proposal will provide new insights to the viscous primitive equations as well as their physical applications.
Project Start Year: 2016, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Blowup of the Euler-Poisson Equations
The isentropic compressible Euler-Poisson equations are important mathematical models with applications in astrophysics, cosmology, the semiconductor industry and fluid mechanics, among others. The Euler-Poisson equations are the standard model in cosmology. The singularity formation in the Euler-Poisson equations has been attracting the attention of a number of researchers because of its physical significance and mathematical challenge.

In this project, we study the long time behavior of the solution including the phenomena of finite-time singularity and global existences of the compressible Euler-Poisson equations. We have five approaches to tackle the problem including integration method, energy method, spectral dynamics, exact solutions and variations of classical methods/new methods in this study. We aimed to develop new methods for proving blowup behavior of the Euler-Poisson equations. We believe that new methods and results will be beneficial to the mathematics community and our understanding of the equations, and the methods will provide more tools for other scientists to study the blowup of equations in classical fluid dynamics and astrophysics even for other nonlinear equations of evolution.
Project Start Year: 2015, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Blowup of the Compressible Euler Equations
The singularity formation in fluid mechanics has been attracting the attention of a
number of researchers because of its physical significance and mathematical
challenge. In this project, we are interested in exploring the long time
behavior of the solution including the phenomena of finite-time singularity and global
existence of the compressible Euler equations.
Project Start Year: 2015, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Tin Ka Ping Education Fund for the Mainland Visiting Scholars Exchange Programme 2014/15
The visiting scholar, Prof. Fan Engui from Fudan University, will cooperate with Dr Yuen Manwai for investigating research work on new bounded exact solutions for Euler equations and Navier-Stokes equations. Recently, we first found peakon solutions for the 2D incompressible Euler equations, this should be an interesting result on 2D incompressible Euler equation. We hope to generalize this method to 2D compressible Euler equations and 3D Euler equation next visiting under support of Tin Ka Ping Education Fund. During this visit, five academic seminars by Prof. Fan will be given to the public.
Project Start Year: 2015, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Symmetry Reductions for the Compressible Euler and Navier-Stokes Equations
The compressible Euler and Navier-Stokes systems are equations of evolution which are important mathematical models in fluid dynamics. For a given differential equation of evolution, such as the Euler or Navier-Stokes system, the most fundamental question one may ask is whether there exists a unique solution or not. The finite-time blowup phenomenon of the Euler and Navier-Stokes equations may provide partial answers to these questions. In this proposed project, we are interested in constructing the novel analytical or exact solutions via symmetry reductions, including quasi-solution methods, similarity reduction methods, characteristic methods et al. Mathematical properties of the solutions such as blowup phenomenon, stability, oscillation et al, will be further analyzed. Finally, numerical simulations and figures will be implemented to explain the meanings of the solutions obtained and their physical applications. The study of mathematical properties of analytical solutions will help to understand the finite-time blowup phenomenon of the Euler and Navier-Stokes equations. The investigations in this proposal will provide new insights to the Euler and Navier-Stokes systems as well as their physical applications.
Project Start Year: 2014, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Evolution of Flows for the Euler or Navier-Stokes System
The compressible Euler and Navier-Stokes systems are important mathematical models in fluid dynamics. In astrophysics, the formation of black-holes and the evolution of gaseous stars remain one of the fundamental and important questions to which, no universally acceptable answer has been agreed on yet. Many believe that the phenomenon of the finite time blowup of solutions of systems may provide plausible explanations to these matters. In this proposed project, we are interested in the novel analytical or exact solutions of fluids as well as their qualitative behaviors. The class of blowup solutions may hold the key to understanding the process of how fluids or gases evolve from a regular to a singular state. Here, both analytic (symmetry reduction and Lie-group analysis) and numerical approaches will be adopted to seek new solutions to the systems. Our study of the Euler and the Navier-Stokes systems will expand the knowledge base of this subject.
Project Start Year: 2013, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Blowup and Global Existence of the Camassa-Holm Equation
In this proposed study, original results about the blowup or global existence of the Camassa-Holm equation and its related systems are expected to be obtained. We aim to search new methods or approaches for proving the blowup or global existence of the Camassa-Holm equation. Meanwhile, we expect that these methods or approaches can be applied to other related systems and can generate more results from the existing work of the other mathematicians.
Project Start Year: 2013, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Blowup Phenomena for the Compressible Euler Equations
The N-dimensional isentropic compressible Euler and Euler-Poisson equations are important mathematical models with applications in astrophysics, cosmology, the semiconductor industry and fluid mechanics, among others. It is interesting to see whether the three-dimensional Euler or Navier-Stokes equations generate blowup phenomena. The Euler system is a special case of the Navier-Stokes system. Thus, investigating the blowup problem in the Euler system may provide insight into the Navier-Stokes blowup problem. As the Euler-Poisson system is also an extension of the Euler system, we study its blowup problem simultaneously.
Project Start Year: 2013, Principal Investigator(s): YUEN, Man Wai 阮文威

 
Analytical Solutions for 2-component Shallow Water System
In the proposal, we study the symmetry reduction of some shallow water equations, for example the 2-component Camassa–Holm, Dullin-Gottwald-Holm, Degasperis-Procesi, Fornberg-Whitham and Degasperis-Procesi Equations. The shallow water systems are important to study the ocean dynamics. In details, we would like to study the analytical or exact solutions for the above shallow water equations. We want to apply the new solutions for modeling the drifting phenomena of the ocean fluids, like Tsunamis. There will be a lot of potential applications of the new constructed solutions for real world applications. For the analytical or exact solutions, scientists can use it as reference solutions to check the numerical methods. Therefore, they can design more accurate methods for modeling the real cases.
Project Start Year: 2013, Principal Investigator(s): YUEN, Man Wai 阮文威

 
The Perturbational Solutions for the Euler and Navier-Stokes Equations and their Related Systems
Some exact solutions were already given for the compressible Euler equations and related systems. In this proposed project, we want to find out the possibilities of some perturbational solutions which the neighborhood of the exact solutions. Some functional techniques will be applied to structure a more general class of the solutions both implicitly or explicitly. It is useful to demonstrate the existence of such solutions for the numerical simulations for the scientists and engineers. It will be provided the concrete examples to valid their computing methods.
Project Start Year: 2012, Principal Investigator(s): YUEN, Man Wai 阮文威

 
The Study of a Class of Analytical Blowup Solutions of Euler or Navier-Stokes Equations
The Euler or Navier-Stokes equations are the fundamental equations for the fluid dynamics. We study the symmetry reduction of the Euler or Navier-Stokes equations. New analytical solutions are expected to construct to understand the blowup phenomena of the systems.
Project Start Year: 2012, Principal Investigator(s): YUEN, Man Wai 阮文威