On 2D incompressible Boussinesq systems: Global stabilization under dynamic boundary conditions

Abstract

This paper studies the stability of large data solutions to the 2D fully/partially dissipative Boussinesq systems on the unit square subject to various types of boundary conditions, including dynamic Couette flow. It is shown that under suitable conditions on the boundary data, solutions starting in H3 exist globally in time and the differences between the solutions and their corresponding boundary data converge to zero in certain topology as time goes to infinity. There is no smallness restrictions on initial data.