摘要：TheBoussinesq equations concerned here model geophysical flows such asatmospheric fronts and ocean circulations. In addition, they play an importantrole in the study of Rayleigh-Benard convection. Mathematically the 2DBoussinesq equations serve as a lower-dimensional model of the 3D hydrodynamicsequations.  The global regularity problem on the 2D Boussinesqequations with partial or fractional dissipation has attracted considerableattention in the last few years. This talk presents recent developments inthis direction. In particular, we detail the global regularity result onthe 2D Boussinesq equations with vertical dissipation as well as somerecent work on the 2D Boussinesq equations with general criticaldissipation. If time permits, we will also briefly discuss the regularity problemon the partially dissipated Boussinesq equations in a bounded domain.