Existence results for the radiation hydrodynamic equations with degenerate viscosity coefficients and vacuum

In this paper, we consider the compressible isentropic radiation hydrodynamic equations with density-dependent viscosity coefficients when the initial data are arbitrarily large and include vacuum at least appearing in the far field. Based on some reasonable assumptions for the radiation coefficients, we firstly establish the existence of a unique local regular solution, which implies the existence of the local strong solution. Moreover, we show a blow-up criterion for the regular solution that we obtained.