Dr YUEN, Man Wai   阮文威
Assistant Professor
Department of Mathematics and Information Technology
Phone No: (852) 2948 8973
Email: yuenmw@eduhk.hk
Contact
ORCiD
0000-0002-5035-3555
Phone
(852) 2948 8973
Email
yuenmw@eduhk.hk
Scopus ID
35093581700
ResearcherID
B-1210-2008
Research Interest

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), Analytical and Exact Solutions, Mathematical Methods in Fluids, Classical Cosmology

Math Education: Mathematics Teachers' Competency, STEM Education, Methodology of Mathematics, Mathematical Reasoning

Teaching Interest

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 Eqautions and Dynamical Modeling

12. MTH 4900 Honor Projects II

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

External Appointment

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, (which is ranked 821/1779 in Medicine (miscellaneous) by SCImago Journal Rank (SJR indicator) 2015), 2013-16.

2. 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.)

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

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

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

Professional 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 from 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 has been the field exprience coordinator (Math) since 2014. Dr Yuen has been the group leader in the departmental research group, Professional Development Group for Hong Kong Mathematics Teachers since 2019.

Dr. Yuen's research interest is applied analysis of nonlinear partial differential equations, specially involving blowup phenomena and similar solutions. Dr. Yuen's 65 journal papers (with 58 SCI or SCIE) were published by 31 international Math and Physics journals, including Journal of Mathematical Analysis and Applications, Communications in Nonlinear Science and Numerical Simulation, Journal of Mathematical Physics, Physics Letters A, Nonlinear Analysis, Applied Mathemtics Letters and Studies in Applied Mathematics. His published papers have accumulated 405 citations and a H-index 12 from Scopus. In particular, the paper, "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" is ranked as a highly cited paper by Web of Science in March/April 2020.

Meanwhile, he has also published 2 academic books. He is also an editorial member of the International Journal of Numerical Methods and Applications; 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

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 Interest

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), Analytical and Exact Solutions, Mathematical Methods in Fluids, Classical Cosmology

Math Education: Mathematics Teachers' Competency, STEM Education, Methodology of Mathematics, Mathematical Reasoning

Teaching Interest

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 Eqautions and Dynamical Modeling

12. MTH 4900 Honor Projects II

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

External Appointment

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, (which is ranked 821/1779 in Medicine (miscellaneous) by SCImago Journal Rank (SJR indicator) 2015), 2013-16.

2. 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.)

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

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

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

Selected Output

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
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.

Project

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 t . . .
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
 
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
 
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 mathematical . . .
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
 
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
 
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 t . . .
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 controllin . . .
Project Start Year: 2018, 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
 
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-com . . .
Project Start Year: 2017, 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 com . . .
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 . . .
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, constructi . . .
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 investigati . . .
Project Start Year: 2016, 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
 
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 . . .
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 . . .
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 . . .
Project Start Year: 2014, 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. . . .
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 b . . .
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
 
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 ana . . .
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 b . . .
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