# On weak solutions to the problem of a rigid body with a cavity filled with a compressible fluid, and their asymptotic behavior

## TL;DR

This paper proves the existence and uniqueness of weak solutions for a coupled rigid body and compressible fluid system, analyzing their long-term behavior and convergence to a steady state under specific conditions.

## Contribution

It establishes the existence of weak solutions and a weak-strong uniqueness result, providing insights into the asymptotic behavior of the system.

## Key findings

- Weak solutions exist for the coupled system.
- Weak-strong uniqueness holds under certain conditions.
- Solutions tend to a unique steady state over time.

## Abstract

We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows us to completely characterize, under certain physical assumptions, the asymptotic behavior in time of the weak solution corresponding to smooth data of restricted "size" and show that it tends to a uniquely determined steady-state.