The two-dimensional Boussinesq equations with partial or fractional dissipation
摘要：The Boussinesq equations concerned here model geophysical flows such as atmospheric fronts and ocean circulations. In addition, they play an important role in the study of Rayleigh-Benard convection. Mathematically the 2D Boussinesq equations serve as a lower-dimensional model of the 3D hydrodynamics equations. The global regularity problem on the 2D Boussinesq equations with partial or fractional dissipation has attracted considerable attention in the last few years. This talk presents recent developments in this direction. In particular, we detail the global regularity result on the 2D Boussinesq equations with vertical dissipation as well as some recent work on the 2D Boussinesq equations with general critical dissipation. If time permits, we will also briefly discuss the regularity problem on the partially dissipated Boussinesq equations in a bounded domain.