  We consider the system of equations modeling the free motion of a rigid body
with a cavity filled by a viscous (Navier-Stokes) liquid. We give a rigorous
proof of Zhukovskiy's Theorem, which states that in the limit of time going to
infinity, the relative fluid velocity tends to zero and the rigid velocity of
the full structure tends to a steady rotation around one of the principle axes
of inertia.
  The existence of global weak solutions for this system was established
previously. In particular, we prove that every weak solution of this type is
subject to Zhukovskiy's Theorem. Independently of the geometry and of
parameters, this shows that the presence of fluid prevents precession of the
body in the limit. In general, we cannot predict which axis will be attained,
but we show stability of the largest axis and provide criteria on the initial
data which are decisive in special cases.
