Initial layer associated with Boussinesq systems for thermosolutal convection

Abstract

This article concerns the behavior of the initial layer appearing at large Prandtl number in Boussinesq equations with the ill initial data. By using the asymptotic expansion methods of singular perturbation theory, we establish an approximate solution and the rate of convergence as the Prandtl number tends to infinity.Our results improve the existing ones concerning thermosolutal convection.