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=ρβ, 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 T2 and the whole space R2 (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Vaǐgant-Kazhikhov model of compressible Navier-Stokes equations.