Global well-posedness of the strong solutions to the two-dimensional full compressible magnetohydrodynamics equations with large viscosity

In this paper, the initial-boundary value problem for the two-dimensional viscous, compressible and heat-conducting magnetohydrodynamics (MHD) equations with vacuum is considered. We show that the strong solution exists globally in the time provided the viscosity coefficient μ is suitably large, and there is no small restriction on the initial data. As a result, we extend the works given by Li and Shang [ 20 ] for the full compressible Navier–Stokes equations and by Liu [ 25 ] for the isentropic compressible MHD equations.