Existence and uniqueness of the boussinesq equations for MHD convection

Abstract

This paper is concerned with the Boussinesq-MHD system with constant viscosity, thermal diffusivity, and electrical conductivity. The existence of this Boussinesq-MHD system was estimated by Littlewood-Paley decomposition, Bony’s para product and commutator estimates. Meanwhile, the uniqueness was estimated by Gronwall inequality. In this paper, the space is the optimal Sobolev spaces for the Boussinesq-MHD system.