Viscous limit to 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 as the heat-conductivity coefficient κ tends to zero, provided that the viscosity μ is higher order than the heat-conductivity κ or the same order as κ. Here we have no need to restrict the strength of the contact discontinuity to be small.