Abstract: 2D Boussinesq system models the natural convection
 of incompressible fluid. The model also serves as the most commonly
 used approximate model for the 3D incompressible Navier-Stokes equation, sharing the key vortex stretching effects. In a joint work with Lai   and Zhao, we proved the global regularity of the classical solution to the initial boundary value problem with no-slip boundary condition. Joint with S. Bianchini, we are able to show that the solution converges to equilibrium in large time.