Inertial Motions of a Rigid Body with a Cavity Filled with a Viscous Liquid

We study inertial motions of the coupled system, ${\mathscr{S}} , constituted by a rigid body containing a cavity entirely filled with a viscous liquid. We show that for arbitrary initial data having only finite kinetic energy, every corresponding weak solution (à la Leray–Hopf) converges, as time goes to infinity, to a uniform rotation, unless two central moments of inertia of {\mathscr{S}} coincide and are strictly greater than the...