ZERO DISSIPATION LIMIT TO RAREFACTION WAVES FOR THE ONE-DIMENSIONAL NAVIER-STOKES EQUATIONS OF COMPRESSIBLE ISENTROPIC GASES

We study the zero dissipation limit problem for the one-dimensional Na vier-Stokes equations of compressible, isentropic gases in the case th at the corresponding Euler equations have rarefaction wave solutions. We prove that the solutions of the Navier-Stokes equations with center ed rarefaction wave data exist for all time, and converge to the cente red rarefaction waves as the viscosity vanishes, uniformly away from t he initial discontinuities. In the case that either the effects of ini tial layers are ignored or the rarefaction waves are smooth, we then o btain a rate of convergence which is valid uniformly for all time. Our method of proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure.