Strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection without thermal diffusion

Abstract

We are concerned with the Cauchy problem of nonhomogeneous Boussinesq equations for magnetohydrodynamics convection in $\mathbb{R}^2$. We show that there exists a unique local strong solution provided the initial density, the magnetic field, and the initial temperature decrease at infinity sufficiently quickly. In particular, the initial data can be arbitrarily large and the initial density may contain vacuum states.

Keywords

• nonhomogeneous boussinesq-mhd system
• strong solutions
• cauchy problem