Department of Mathematics Florida International University Miami, FL 33199, USA Phone number: (305)348-6247 Office: DM 433B E-mail: caoc@fiu.edu

EDUCATION

Ph.D. in Applied Mathematics, 1999. University of California, Irvine.

TEACHING

MAC 2311 Calculus I
course information,
Syllabus

MAP 2302 Differential Equations
course information,
Syllabus

AREAS of INTEREST

PUBLICATIONS

1. Gevrey Class Regularity for the Solution of the Navier--Stokes Equations on the Rotating two Dimensional Sphere
(with M. Rammaha and E.S. Titi), Zeitschrift fur Augewandte Mathematik und Physik (ZAMP), 50, 341--360, 1999.

2. Gevrey Regularity for Nonlinear Analytic Parabolic Equations on the Sphere
(with M. Rammaha and E.S. Titi), Journal of Dynamics and Differential Equations, 12, 411--433, 2000.

3. Numerical Criterion for the Stabilization of Steady States of the Navier--Stokes Equations
(with I.G. Kevrekidis and E.S. Titi), Indiana Math. J., 50, 37--96, 2001.

4. Asymptotic Behavior of Viscous 1--D Conservation Laws with Neumann Boundary Conditions
(with E.S. Titi), Mathematics & Mathematics Education, 206--224, 2002.

5. 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, 198-233, 2003

6. Traveling wave solutions to a class of 1+1 nonlinear shallow water wave-like wave models
(with D.D. Holm and E.S. Titi), Journal of Dynamics and Differential Equations, 16, 167--178, 2004

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

8. On the Clark--alpha model of turbulence: global regularity and long--time dynamics
(with D.D. Holm and E.S. Titi), Journal of Turbulence, number 19, 1--11, 2005.

9. Global well-posedness the Three-dimensional Viscous Primitive Equations of Large Scale Ocean and Atmosphere Dynamics
(with E.S. Titi), Annals Mathematics 166, 245--267, 2007.

10. Regularity criterion of solutions for Three--Dimensional Turbulent Channel Flows,
(with J. Qin and E.S. Titi), Comm. PDE 33, 419--428, 2008.

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

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

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

14. The 2D Boussinesq equations with vertical viscosity and vertical diffusivity,
(with D. Adhikari and Jiahong Wu), J. Differential Equations 249, 1078–1088, 2010.

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

16. Global regularity results for the 2D Boussinesq equations with vertical dissipation,
(with D. Adhikari, Jiahong Wu), J. Differential Equations 251, 1637--1655, 2011.

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