  We obtain estimates of all components of the velocity of a 3D rigid body
moving in a viscous incompressible fluid without any symmetry restriction on
the shape of the rigid body or the container. The estimates are in terms of
suitable norms of the velocity field in a small domain of the fluid only,
provided the distance $h$ between the rigid body and the container is small. As
a consequence we obtain suitable differential inequalities that control the
distance $h$. The results are obtained using the fact that the vector field
under investigation belongs to suitable function spaces, without any use of
hydrodynamic equations.
