We consider an initial-boundary value problem for the equations of one-dimensional motions of a compressible viscous heat-conducting gas coupled with radiation through a radiative transfer equation. Assuming suitable hypotheses on the transport coefficients, we prove that the problem admits a unique weak solution.
"Global Weak Solutions to the 1D Compressible Navier-Stokes Equations with Radiation." Commun. Math. Anal. 8 (3) 23 - 65, 2010.