Vanishing Viscosity Limit to Rarefaction Waves for the Navier-Stokes Equations of One-Dimensional Compressible Heat-Conducting Fluids

We prove the solution of the Navier-Stokes equations for one-dimensional compressible heat-conducting fluids with centered rarefaction data of small strength exists globally in time, and moreover, as the viscosity and heat-conductivity coefficients tend to zero, the global solution converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly away from the initial discontinuity.