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

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.