Global well-posedness for the two dimensional compressible MHD equations with large data

In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $μ$ is a positive constant and the bulk viscosity $λ$ is the power function of the density, that is, $λ(ρ)=ρ^β$ with $β>3$, then the two dimensional compressible MHD system with the periodic boundary conditions on the torus $\mathbb{T}^2$ have a unique global classical solution $(ρ, u,H)$. In this work we extended the results about compressible Navier-Stokes equations in \cite{Karzhikhov} to compressible MHD equations by applying several new techniques to overcome the coupling between velocity and magnetic field.

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