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We consider the inertial motion of a rigid body with an interior cavity thatis completely filled with a viscous incompressible fluid. The equilibria of thesystem are characterized and their stability properties are analyzed. It isshown that equilibria associated with the largest moment of inertia arenormally stable, while all other equilibria are normally hyperbolic. We showthat every Leray-Hopf weak solution converges to an equilibrium at anexponential rate. In addition, we determine the critical spaces for thegoverning evolution equation, and we demonstrate how parabolic regularizationin time-weighted spaces affords great flexibility in establishing regularity ofsolutions and their convergence to equilibria.

A maximal regularity approach to the study of motion of a rigid body with a fluid-filled cavity