CHONGSHENG CAO


Department of Mathematics
Florida International University
Miami, FL 33199
U. S. A.

Office: DM 433B
Phone: 305-348-6247
Email: caoc@fiu.edu



TEACH (SPRING 2020):

MAP 2302 - ODE
Syllabus
Course Information

MAC 2312 - Calculus II
Syllabus
Course Information

RESEARCH:

Nonlinear Partial Differential Equations
Nonlinear Dynamical Systems.
Control Theory.
Fluid Dynamics.
Geophysics.
Computational Mathematics.

Recent Publications:

1. Global Well--posedness and Finite Dimensional Global Attractor for a 3--D Planetary Geostrophic Viscous Model, (with E.S. Titi), Comm. Pure Appl. Math. 56 (2003), 198-233.

2. A ``horizontal" hyper--diffusion $3-D$ thermocline planetary geostrophic model: well-posedness and long time behavior, (with E.S. Titi and M. Ziane), Nonlinearity 17 (2004), 1749-1776.

3. Global Well-posedness of the Three-dimensional Viscous Primitive Equations of Large Scale Ocean and Atmosphere Dynamics, (with E.S. Titi), Annals of Mathematics, 165 (2007), 245-267.

4. Regularity criteria for the three--Dimensional Navier-Stokes equations, (with E.S. Titi), Indiana Univ. Math. J. 57 (2008), 2643-2662.

5. Sufficient conditions for the regularity to the 3D Navier-Stokes equations, Discrete and Continuous Dynamical Systems Series A, 26 (2010), 1141-1151.

6. Two regularity criteria for the 3D MHD equations, (with Jiahong Wu), Journal of Differential Equations 248 (2010), 2263-2274.

7. Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion, (with Jiahong Wu), Advances in Mathematics 226 (2011), 1803-1822.

8. Global regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor, (with E.S. Titi), Arch. Ration. Mech. Anal. 202 (2011) , 919-932.

9. Global well-posedness of the 3D primitive equations with partial vertical turbulence mixing heat diffusion, (with E.S. Titi), Comm. Math. Phys. 310 (2012), 537-568.

10. Global regularity for the 2D anisotropic Boussinesq equations with vertical dissipation, (with Jiahong Wu), Arch. Ration. Mech. Anal. 208(2013), 985-1004.

11. Global well-posedness of an inviscid three-dimensional Pseudo-Hasegawa-Mima model, (with A. Farhat, E.S. Titi), Comm. Math. Phys. 319(2013), 195-229.