Zero dissipation limit to strong contact discontinuity for the 1-D compressible Navier-Stokes equations

In this paper, we study the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations. We prove that if the solution of the inviscid Euler equations is piecewise constants with a contact discontinuity, then there exist smooth solutions to the Navier-Stokes equations which converge to the inviscid solution away from the contact discontinuity at a rate of kappa(1/4) as the heat-conductivity coefficient kappa tends to zero, provided that the viscosity mu is of higher order than the heat-conductivity kappa. Without loss of generality, we set mu 0. Here we have no need to restrict the strength of the contact discontinuity to be small. (C) 2009 Elsevier Inc. All rights reserved.