On some large global solutions for the compressible magnetohydrodynamic system

TL;DR

This paper proves the global well-posedness of the compressible magnetohydrodynamic system in critical Besov spaces under small initial data and parameter conditions, ensuring unique solutions exist for all time.

Contribution

It establishes the first global existence and uniqueness results for the compressible MHD system in critical Besov spaces with specific smallness conditions.

Findings

Global well-posedness under small initial data

Unique solutions exist for all time

Conditions relate viscosity and magnetic diffusion coefficients

Abstract

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then compressible magnetohydrodynamic system has a unique global solution.