  The stability of solutions under periodic perturbations for both inviscid and
viscous conservation laws is an interesting and important problem. In this
paper, a large-amplitude viscous shock under space-periodic perturbation for
the isentropic Navier-Stokes equations is considered. It is shown that if the
initial perturbation around the shock is suitably small and satisfies a
zero-mass type condition (2.17), then the solution of the N-S equations tends
to the viscous shock with a shift, which is partially determined by the
periodic oscillations. In other words, the viscous shock is nonlinearly stable
even though the perturbation oscillates at the far fields. The key point is to
construct a suitable ansatz $ (\tilde{v},\tilde{u}) $, which carries the same
oscillations of the solution $ (v,u) $ at the far fields, so that the
difference $ (v-\tilde{v},u-\tilde{u}) $ belongs to the $ H^2(R) $ space for
all $ t\geq 0. $
