Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum

Abstract

In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $\hat{I}¼=const.$ and $\hat{I}»=\ddot{I}{}^2,{\hat{I}}^2>1$ (Vaǐgant-Kazhikhov Model) for the viscosity coefficients, the global existence and uniqueness of classical solutions to the initial value problem is established on the torus ${\mathbb{T}}^2$ and the whole space ${\mathbb{R}}^2$ (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Vaǐgant-Kazhikhov model of compressible Navier-Stokes.