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 $\mu =const.$ and $\lambda ={\rho }^{\beta },\beta >1$ (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.

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