  We prove the nonlinear stability of the planar viscous shock up to a
time-dependent shift for the three-dimensional (3D) compressible Navier-Stokes
equations under the generic perturbations, in particular, without zero mass
conditions. Moreover, the time-dependent shift function keeps the shock profile
shape time-asymptotically. Our stability result is unconditional for the weak
planar Navier-Stokes shock. Our proof is motivated by the $a$-contraction
method (a kind of weighted $L^2$-relative entropy method) with time-dependent
shift introduced in [10,11,13] for the stability of viscous shock in
one-dimensional (1D) case. Instead of the classical anti-derivative techniques,
we perform the stability analysis of planar Navier-Stokes shock in original
$H^2$-perturbation framework and therefore zero mass conditions are not
necessarily needed, which, in turn, brings out the essential difficulties due
to the compressibility of viscous shock. Furthermore, compared with 1D case,
there are additional difficulties coming from the wave propagation along the
multi-dimensional transverse directions and their interactions with the viscous
shock. To overcome these difficulties, a multi-dimensional version sharp
weighted Poincar${\rm \acute{e}}$ inequality (see Lemma 3.1), $a$-contraction
techniques with time-dependent shift, and some essential physical structures of
the multi-dimensional Navier-Stokes system are fully used.
