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In this paper, we study the global well-posedness of classical solutions tothe 2D compressible MHD equations with large initial data and vacuum. With theassumption $\mu=const.$ and $\lambda=\rho^\beta,~\beta>1$(Va\v{i}gant-Kazhikhov Model) for the viscosity coefficients, the globalexistence and uniqueness of classical solutions to the initial value problem isestablished on the torus $\mathbb{T}^2$ and the whole space $\mathbb{R}^2$(with vacuum or non-vacuum far fields). These results generalize the previousones for the Va\v{i}gant-Kazhikhov model of compressible Navier-Stokes.

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