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

Abstract

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 $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the density, that is, $\lambda (\rho )={\rho }^{\beta }$ with $\beta >3$, then the two dimensional compressible MHD system with the periodic boundary conditions on the torus ${\mathbb{T}}^2$ have a unique global classical solution $(\rho ,u,H)$. 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.

43 pages

Cited by in corpus (1)

• Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces