On asymptotic stability of the 3D Boussinesq equations without thermal conduction

Abstract

We investigate the asymptotic stability of solution to Boussinesq equations without thermal conduction with the initial data near a specific stationary solution in the three--dimensional domain $\Omega = \mathbb{R}^{2}\times (0,1)$. It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.