  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.
