Stratified Boussinesq equations with a velocity damping term

Abstract

We consider an initial value problem of the multi-dimensional Boussinesq equations with velocity damping for strongly stratified fluids. We prove the global-in-time existence of the classical solution to the stratified damped Boussinesq equations with initial data near the stationary stratified solution (v(s), rho(s), p(s)) = (0, ..., 0, x(d), x(d)(2)/2). We also show the asymptotic stability of the solutions near the stratified solution and obtain the temporal decay for the fluid velocity and the temperature by providing estimates for the Green function associated with the linear operator in any dimension.