Global existence of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains

TL;DR

This paper proves the global existence of strong solutions for the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains, extending previous bounded domain results.

Contribution

It generalizes Kazhikhov's bounded domain theory to unbounded domains for the MHD equations with large initial data.

Findings

Global strong solutions exist for large initial data in unbounded domains.

The results extend Kazhikhov's theory from bounded to unbounded domains.

The solutions satisfy conditions similar to those in bounded domain theory.

Abstract

In one-dimensional unbounded domains, we consider the equations of a planar compressible magnetohydrodynamic (MHD) flow with constant viscosity and heat conductivity. More precisely, we prove the global existence of strong solutions to the MHD equations with large initial data satisfying the same conditions as those of Kazhikhov's theory in bounded domains (Kazhikhov 1987 Boundary Value Problems for Equations of Mathematical Physics (Krasnoyarsk)). In particular, our result generalizes the Kazhikhov's theory for the initial boundary value problem in bounded domains to the unbounded case.