  In this paper, we study the vanishing viscosity of the isentropic
compressible Navier-Stokes equations with density dependent viscous coefficient
in the presence of the shock wave. Given a shock wave to the corresponding
Euler equations, we can construct a sequence of solutions to one-dimensional
compressible isentropic Navier-Stokes equations which converge to the shock
wave as the viscosity tends to zero. The proof is given by an elementary energy
method.
