Global large solutions of magnetohydrodynamics with temperature-dependent heat conductivity

Abstract

In this paper, we consider an initial boundary value problem for the magnetohydrodynamic compressible flows. By assuming that the heat conductivity depends on temperature with κ (θ) = θ q , q > 0, we prove the existence and uniqueness of global strong solutions with large initial data and show that neither shock waves nor vacuum and concentration of mass in the solutions are developed in a finite time.