Global solutions to the one-dimensional compressible Navier-Stokes equation with radiation

We investigate the global existence of a smooth solution to the one-dimensional compressible Navier-Stokes equation with radiation. The transport coefficients μ and κ are both degenerate. The pressure p(t,x) varies in different temperature regions. Our discussion considers the case when pressure p(t,x) satisfies the Benedict-Webb-Rubin equation at high temperature; the result obtained for this problem is presented for the first time.