## Dr. Suen Chun Kit Anthony

Associate Professor

### Profile

2007 - 2012, Ph.D. in mathematics, Indiana University Bloomington, USA

2005 - 2007, M.Phil. in mathematics, The Chinese University of Hong Kong, Hong Kong

2002 - 2005, B.Sc. in mathematics, The Chinese University of Hong Kong, Hong Kong

Please refer to my personal homepage for more updated information.

### Research Interests

My research focuses primarily on the existence theory and large-time behaviour of solutions of certain systems of partial differential equations. In particular, I am interested in the multidimensional compressible or incompressible fluid flow models with applications to Navier-Stokes equations, magnetohydrodynamics (MHD) and magneto-geostrophic (MG) equation. I also study mathematical biology such as chemotaxis and blood flow modelling.

### Selected Outputs

Journal Publications

- Suen, A. (2022).
*Global regularity for the 3D compressible magnetohydrodynamics with general pressure*.*Discrete and Continuous Dynamical Systems - Series A*,*42(6)*, 2927-2943 - Suen, A. (2022).
*Some Serrin type blow-up criteria for the three-dimensional viscous compressible flows with large external potential force*.*Mathematical Methods in the Applied Sciences*,*45(4)*, 2072-2086 - Suen, A. (2022).
*Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure*.*Zeitschrift für angewandte Mathematik und Physik*,*73(1)*, 1-19 - Suen, A. (2021).
*Existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force*.*Journal of Differential Equations*,*299*, 463-512 - Friedlander, S. and Suen, A. (2021).
*Correction to: Wellposedness and Convergence of Solutions to a Class of Forced Non-diffusive Equations with Applications*.*Journal of Mathematical Fluid Mechanics*,*23 (81)*, 1-3 - Friedlander, S. and Suen, A. (2021).
*Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations*.*Archive for Rational Mechanics and Analysis*,*240(3)*, 1431-1485 - Yee, Tat-Leung, Cheung, Ka Luen, Ho, Kwok-Pun & Suen, Chun Kit (2020).
*Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents*.*Mathematical Inequalities & Applications*,*23(4)*, 1509-1528 - Suen, A. (2020). Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy.
*Discrete and Continuous Dynamical Systems - Series A**, 40 (3)*, 1775-1798. - Suen, A. (2020). Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations.
*Journal of Differential Equations**, 268 (6)*, 2622-2671. - Friedlander, S. and Suen, A (2019). Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications.
*Journal of Mathematical Fluid Mechanics**, 21(4)*, 21-50. - Friedlander, S. and Suen, A. (2018). Solutions to a Class of Forced Drift-Diffusion Equations with Applications to the Magneto-Geostrophic Equations.
*Annals of PDE**, 4(2)*, 1-34. - Cheung, K.L. and Suen, A. (2016). Existence and Uniqueness of Small Energy Weak Solution to multi- dimensional compressible Navier-Stokes Equations with Large External Potential Force.
*Journal of Mathematical Physics**, 57 (8), 081513*, 1-19. - Li, T. and Suen, A. (2016). Existence of intermediate weak solution to the equations of three-dimensional chemotaxis systems.
*Discrete and Continuous Dynamical Systems - Series A**, 36 (2)*, 861-875. - Friedlander, S. and Suen, A (2015). Existence, uniqueness and regularity results for the viscous magneto-geostrophic equation.
*Nonlinearity**, 28 (9)*, 3193-3217. - Li, T., Suen, A., Winkler, M. and Xue, C. (2015). Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms.
*Mathematical Models & Methods in Applied Sciences**, vol. 25 (no. 4)*, 721-746. - Suen, A. (2015). Corrigendum: A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density.
*Discrete and Continuous Dynamical Systems - Series A**, vol. 35 (no. 3)*, 1387-1390. - Friedlander, S. and Suen, A (2014). Hölder continuity of solutions to the kinematic dynamo equations.
*Journal of Mathematical Fluid Mechanics**, vol. 16 (no. 4)*, 691-700. - Suen, A. (2014). Existence of global weak solution to Navier-Stokes equations with large external potential force and general pressure.
*Mathematical Methods in the Applied Sciences**, vol. 37 (no. 17)*, 2716-2727. - Suen, A. (2013). A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density.
*Discrete and Continuous Dynamical Systems - Series A**, vol. 33 (no. 8)*, 3791-3805. - Suen, A. (2013). Global Solutions of the Navier-Stokes Equations for Isentropic Flow with Large External Potential Force.
*Zeitschrift für angewandte Mathematik und Physik (ZAMP)**, vol. 64 (no. 3)*, 767-784. - Suen, A. and Hoff, D. (2012). Global low-energy weak solutions of the equations of 3D compressible magnetohydrodynamics.
*Archive for Rational Mechanics and Analysis**, vol. 205 (no.1)*, 27-58. - Suen, A. (2012). Nonexistence of self-similar singularities in the ideal viscoelastic flow.
*Electronic Journal of Differential Equations**, vol. 2012 (no. 93)*, 1-7.

### Research Projects

**Wellposedness and singularity formation of inviscid active scalar equations with even or odd constitutive laws**

This is a RGC funded project through the General Research Fund (GRF) with the amount of HK$653,250. The present project studies an abstract class of inviscid active scalar equations with even or odd constitutive laws. We propose to address the well-posedness and possible formation of finite time singularity, which have applications on various physical models including the magneto-geostrophic equation, incompressible porous media Brinkman equation and surface quasi-geostrophic equation.

Project Start Year: 2023, Principal Investigator(s): SUEN, Chun Kit Anthony 孫俊傑

**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 (SUEN, Chun Kit Anthony 孫俊傑 as Co-Investigator)

**Asymptotic behavior and anomalous dissipation of a general class of forced active scalar equations **

This is a RGC funded project through the General Research Fund (GRF) with the amount of HK$598,015. The present project studies an abstract class of forced active scalar equations with emphasis on well-posedness, long time behaviour and anomalous dissipation, which arises in a variety of physical models including the magneto-geostrophic equation, incompressible porous media Brinkman equation and surface quasi-geostrophic equation.

Project Start Year: 2022, Principal Investigator(s): SUEN, Chun Kit Anthony 孫俊傑

**Wellposedness on some classes of fluid equations **

This project is funded by EdUHK Dean’s Research Fund. The present project will focus on different mathematical questions relating to the wellposedness of certain systems of partial differential equations associated with fluids.

Project Start Year: 2021, Principal Investigator(s): SUEN, Chun Kit Anthony 孫俊傑

**Inviscid limit and long time behaviour for a class of active scalar equations with physical applications **

This is a RGC funded project through the General Research Fund (GRF) with the amount of HK$396,967. The present project studies an abstract class of active scalar equations with emphasis on the vanishing viscosity limit and long time behaviour, as a key step in studying some physical models which include the magneto-geostrophic equation and incompressible porous media Brinkman equation.

Project Start Year: 2021, Principal Investigator(s): SUEN, Chun Kit Anthony 孫俊傑

**Inequalities and Operators on Morrey Type Spaces with Applications to the Euler Equations under Damping **

This project will study important operators and establish related inequalities on Morrey Type Spaces, and investigate their applications to the Euler Equations under Damping.

Project Start Year : 2019 Chief Investigator(s) : CHEUNG, Ka Luen 張家麟 (Dr SUEN, Chun Kit Anthony 孫俊傑 as Co-Investigator)

**Wellposedness and Vanishing Diffusion Parameters Limits of the Magneto-geostrophic Equation **

This is a RGC funded project through the Early Career Scheme (ECS) with the amount of HK$409,423. The present project focuses on different mathematical questions relating to a three-dimensional active scalar equation called the magneto-geostrophic (M **. . .**

Project Start Year : 2017 Chief Investigator(s) : SUEN, Chun Kit Anthony 孫俊傑

**Existence of intermediate weak solutions to the equations of multi-dimensional chemotaxis **

This project is funded by HKIEd Start-up Research Grant. We study the global-in-time existence of intermediate weak solutions of the equations of chemotaxis system in a bounded domain with small initial chemical concentration.

Project Start Year : 2015 Chief Investigator(s) : SUEN, Chun Kit Anthony 孫俊傑

**Existence, uniqueness and regularity results for the viscous magneto-geostrophic equations**

This project is funded by HKIEd Dean’s Research Fund. The present project will focus on different mathematical questions relating to the existence, uniqueness, regularity and large-time behavior of solutions of certain systems of partial differential **. . .**

Project Start Year : 2015 Chief Investigator(s) : SUEN, Chun Kit Anthony 孫俊傑

**Global existence and propagation of singularities of solutions to the multi-dimensional incompressible MHD with zero resistivity and discontinuous initial data **

This project is funded by HKIEd Internal Research Grant. We study the global existence and propagation of singularities of weak solutions of the incompressible magneto-hydrodynamics (MHD) with zero resistivity in two spatial dimensions.

Project Start Year : 2015 Chief Investigator(s) : SUEN, Chun Kit Anthony 孫俊傑

## Dr. Suen Chun Kit Anthony

Associate Professor