Global weak solutions to the one-dimensional compressible heat-conductive MHD equations without resistivity

TL;DR

This paper proves the existence, uniqueness, and stability of global weak solutions for the one-dimensional compressible heat-conductive MHD equations without resistivity, advancing understanding of such fluid models.

Contribution

It establishes the existence and Lipschitz continuous dependence of global weak solutions for these equations, which was previously unresolved.

Findings

Existence of global weak solutions

Uniqueness and stability of solutions

Lipschitz continuous dependence on initial data

Abstract

We investigate the initial-boundary value problem for one-dimensional compressible, heat-conductive, non-resistive MHD equations of viscous, ideal polytropic fluids in the Lagrangian coordinates. The existence and Lipschitz continuous dependence on the initial data of global weak solutions are established. Uniqueness of weak solutions follows as a direct consequence of stability.