Weak solutions to a full compressible magnetohydrodynamic flow interacting with thermoelastic structure

TL;DR

This paper proves the existence of weak solutions for a complex two-dimensional fluid-structure interaction involving a full compressible magnetohydrodynamic fluid and a thermoelastic shell, accounting for heat exchange and coupling effects.

Contribution

It introduces a novel mathematical framework for analyzing coupled magnetohydrodynamic and thermoelastic systems with a moving interface in two dimensions.

Findings

Existence of weak solutions established for the coupled system.

Development of domain extension and operator splitting techniques.

Handling of heat exchange and interface conditions in the analysis.

Abstract

This paper is concerned with an interaction problem between a full compressible, electrically conducting fluid and a thermoelastic shell in a two-dimensional setting. The shell is modelled by linear thermoelasticity equations, and encompasses a time-dependent domain which is filled with a fluid described by full compressible (non-resistive) magnetohydrodynamic equations. The magnetohydrodynamic flow and the shell are fully coupled, resulting in a fluid-structure interaction problem that involves heat exchange. We establish the existence of weak solutions through domain extension, operator splitting, decoupling, penalization of the interface condition, and appropriate limit passages.