  We consider the system constituted by a hollow rigid body whose cavity
contains a homogeneous rigid ball, and let the gap between the solids be
entirely filled by a viscous incompressible fluid. We investigate the free
rotations of the whole system, i.e., motions driven only by the inertia of the
fluid-solids system once an initial angular momentum is imparted on the whole
system. We prove the existence of global weak solutions and local strong
solutions to the equations of motion. In addition, we prove that the fluid
velocity as well as the inner core angular velocity relative to the outer solid
converge to zero as time approaches infinity.
