Department of Mathematics, Hong Kong University of Science and Technology
Tel: +852 23588572
Address: Room 3450, Department of Mathematics
Clear Water Bay, Kowloon, Hong Kong
Analysis of Partial Differential Equations especially arising from fluid mechanics
2020-2023 Hong Kong RGC Grant GRF 16308820
Gold Medal for the Second National PDE Doctoral Forum
Spring term 2018-2019: MATH 1014 - Calculus II
Fall term 2019-2020: MATH 1013 - Calculus IB
Fall term 2020-2021: MATH 1013 - Calculus IB
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.