Stability of strong solutions to the full compressible magnetohydrodynamic system with non-conservative boundary conditions

TL;DR

This paper establishes the stability and uniqueness of strong solutions to the full compressible magnetohydrodynamic system within a broad class of dissipative measure-valued solutions, under non-conservative boundary conditions.

Contribution

It introduces a DMV-strong uniqueness principle for the MHD system, demonstrating that DMV solutions coincide with strong solutions when they exist.

Findings

Proves stability of strong solutions within DMV framework

Establishes DMV-strong uniqueness principle

Extends analysis to non-conservative boundary conditions

Abstract

We define a dissipative measure-valued (DMV) solution to the system of equations governing the motion of a general compressible, viscous, electrically and heat conducting fluid driven by non-conservative boundary conditions. We show the stability of strong solutions to the full compressible magnetohydrodynamic system in a large class of these DMV solutions. In other words, we prove a DMV-strong uniqueness principle: a DMV solution coincides with the strong solution emanating from the same initial data as long as the latter exists.