  In this paper, we consider the large time behavior of planar shock wave for
3-D compressible isentropic Navier-Stokes equations (CNS) in half space.
Providing the strength of the shock wave and initial perturbations are small,
we proved the planar shock wave for 3-D CNS is nonlinearly stable in half space
with Navier boundary condition.
  The main difficulty comes from the compressibility of shock wave, which leads
to lower order terms with bad sign, see the third line in \cref{C17}. We apply
a decomposition of the solution into zero and non-zero modes: we take the
anti-derivative for the zero mode and obtain the space-time estimates for the
energy of perturbation itself. Then combining the fact that the Poincar\'e
inequality is available for the non-zero mode, we have successfully controlled
the lower order terms with bad sign in \cref{C17}. To overcome the difficulty
that comes from the boundary, we introduce the two crucial estimates on
boundary \cref{CLem0} and fully utilize the property of Navier boundary
conditions, which means that the normal velocity is zero on the boundary and
the fluid tangential velocity is proportional to the tangential component of
the viscous stress tensor on the boundary. Finally, the nonlinear stability is
proved by the weighted energy method.
