Global strong solutions to the planar compressible magnetohydrodynamic   equations with large initial data and vaccum
  This paper considers the initial boundary problem to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. The global existence and uniqueness of large strong solutions are established when the heat conductivity coefficient $\kappa(\theta)$ satisfies \begin{equation*} C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q) \end{equation*} for some constants $q>0$, and $C_1,C_2>0$. 
Jishan Fan, Shuxiang Huang and Fucai Li
math.AP