Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vaccum

TL;DR

This paper proves the global existence and uniqueness of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum, under certain heat conductivity conditions.

Contribution

It establishes the first global strong solution results for these equations with large initial data and vacuum, extending previous work to more general heat conductivity.

Findings

Global strong solutions exist and are unique.

Solutions are valid for large initial data and vacuum conditions.

Heat conductivity bounds are crucial for the results.

Abstract

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 $C_1,C_2>0$.