Viscous limits to piecewise smooth solutions for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids (Q1043671)

The present paper deals with a study of the asymptotic equivalence between the solutions of the compressible Navier-Stokes equations and the compressible Euler equations. The zero dissipation limit problem for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids is investigated. It is shown that the piece-wise smooth solutions of the inviscid Euler equations with finitely many non-interacting shocks satisfying the entropy condition are strong limits of solutions of the one-dimensional Navier-Stokes equations as the viscosity and heat-contactivity coefficients tend to zero.