  Global uniform boundedness of solutions to 3D viscous Primitive equations in
a bounded cylindrical domain with physical boundary condition is proved in
space $H^m$ for any $m\geqslant2$. A bounded absorbing set for the solutions in
$H^m$ is obtained. These results seem rather difficult for the methods recently
developed in [8] and [10]. A completely different approach based on hydrostatic
helmholtz decomposition is presented, which can also be applied to cases with
other different boundary conditions. Several important results about
hydrostatic Leray projector are obtained and utilized. These results are
expected to be of general interest and will be helpful as well for solving some
other problems for 3D viscous Primitive equations which appeared hard
previously for the cases with non-periodic boundary conditions (see e.g. [9]).
