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

We investigate the asymptotic stability of the solutions to Boussinesq equations without heat conduction with the initial data near a specific stationary solution in the three-dimensional domain Ω=ℝ2×(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega = {\mathbb{R}^2} \times (0,1)$$\end{document}. 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.