Stability for the $2\frac12$-D compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow

TL;DR

This paper proves the global existence and exponential decay of strong solutions for a 2.5-dimensional compressible, heat-conducting, non-resistive MHD flow with vertical magnetic field, without requiring a positive background magnetic field.

Contribution

It establishes the global well-posedness and decay rates for a complex MHD system without the need for positive background magnetic field assumptions.

Findings

Proved global existence of strong solutions in Sobolev spaces

Established exponential decay of solutions

Removed the need for positive background magnetic field assumption

Abstract

In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting the intrinsic structure of the system and introducing several new unknown quantities, we overcome the difficulty stemming from the lack of dissipation for density and magnetic field, and prove the global well-posedness of strong solutions in the framework of Soboles spaces $H^3$. In addition, we also get the exponential decay for this non-resistive system. Different from the known results [23], [24], [42], we donot need the assumption that the background magnetic field is positive here.