Regularity and stability results for the 2D Boussinesq equations with partial dissipation

ABSTRACT: The Boussinesq equations concerned here model geophysical fluids as well as the Rayleigh–Bénard convection. This talk is divided into two parts. The first part summarizes recent work on the global-in-time  existence and regularity problem for the the 2D Boussinesq equations with partial or fractional dissipation. The second part presents  the linear and nonlinear stability results on the hydrostatic equilibrium of the 2D Boussinesq equations with only velocity dissipation. This part is based on joint work with C. Doering, K. Zhao and X. Zheng.

HOST: Huiqiang Jiang