On the outer pressure problem of the one-dimensional compressible Navier-Stokes equation with degenerate transport coefficients

This paper is concerned with the initial boundary value problem for the compressible Navier-Stokes system with degenerate transport coefficients. We prove the global existence of large solutions for the outer pressure problem of a viscous, heat-conducting, one-dimensional real gas. The proof is based on several detailed analysis and key a priori estimates on the bounds on the density and temperature.