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

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 $μ=const.$ and $λ=ρ^β,~β>1$ (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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