On the Motion of a Body with a Cavity Filled with Magnetohydrodynamic Fluid

TL;DR

This paper investigates the dynamics of a rigid body with a cavity filled with magnetohydrodynamic compressible fluid, establishing existence, uniqueness, and weak-strong solution principles for the coupled system.

Contribution

It provides the first rigorous proof of global existence and uniqueness of solutions for this complex coupled system involving magnetohydrodynamic fluids and rigid body motion.

Findings

Proved global existence of classical solutions.

Established weak-strong uniqueness principle.

Demonstrated the well-posedness of the coupled system.

Abstract

We study the dynamics of a coupled system, formed by a rigid body with a cavity entirely filled with magnetohydrodynamic compressible fluid. Our aim is to derive the global existence of the unique classical solutions and weak solutions to this system. Moreover, we show the weak-strong uniqueness principle which means that a weak solution coincides with a strong solution on the time existence of a strong solution, provided they emanate from the same initial data.