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

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.