Asymptotic stability of viscous contact wave for the one-dimensional compressible viscous gas with radiation

In this paper, we study the large-time behavior of solutions of the Cauchy problem to a one-dimensional Navier-Stokes-Poisson coupled system, modeling the dynamics of a viscous gas in the presence of radiation. When the far field states are suitably given, and the corresponding Riemann problem for the Euler system admits only a contact discontinuity wave solution with the far field states as Riemann initial data. Then, we can define a “viscous contact wave” for such a Navier-Stokes-Poisson coupled system. Based on elementary energy methods and ellipticity of the equation of the radiation flux, we can prove the “viscous contact wave” is stable provided the strength of the contact discontinuity wave and the perturbation of the initial data are suitably small.