Yuan CAI (蔡圆)

Research Assistant Professor

Department of Mathematics, Hong Kong University of Science and Technology


Contact Information

Tel: +852 23588572

Email: maycai@ust.hk

Address: Room 3450, Department of Mathematics

The Hong Kong University of Science and Technology

Clear Water Bay, Kowloon, Hong Kong


Research Interests:

Analysis of Partial Differential Equations especially arising from fluid mechanics


Awards

2020-2023 Hong Kong RGC Grant GRF 16308820

Gold Medal for the Second National PDE Doctoral Forum


Teaching

Spring term 2018-2019: MATH 1014 - Calculus II

Fall term 2019-2020: MATH 1013 - Calculus IB

Fall term 2020-2021: MATH 1013 - Calculus IB


Publications & Preprints

1. Yuan Cai, Uniform bound of the highest-order energy of the 2D incompressible elastodynamics. Submitted, 2020. Available at arXiv:2010.08718.

2. Yuan Cai and Fan Wang, Global well-posedness of incompressible elastodynamics in three dimensional thin domain. Submitted, 2020.

3. Yuan Cai and Wei Wang, Global well-posedness for the three dimensional simplified inertial Ericksen-Leslie systems near equilibrium. Journal of Functional Analysis. 279 (2020), no. 2, 108521, 38 pp.

4. Yuan Cai, Zhen Lei, Fang-hua Lin and Nader Masmoudi, Vanishing viscosity limit for the incompressible viscoelasticity in two dimensions. Comm. Pure Appl. Math. 72 (2019), no. 10, 2063-2120

5. Yuan Cai and Zhen Lei, Global well-posedness of the incompressible magnetohydrodynamics. Arch. Ration. Mech. Anal. 228 (2018), no. 1, 969-993.

6. Yuan Cai, Zhen Lei and Nader Masmoudi, Global well-posedness for 2D nonlinear wave equations without compact supports. J. Math. Pures Appl. 114 (2018), 211–234.