A Note on a Multi-Dimensional Radiating Gas Model with Nonlinear Radiative Inhomogeneity

Abstract

In this paper, we consider the Cauchy problem of a multi-dimensional radiating gas model with nonlinear radiative inhomogeneity. Such a model gives a good approximation to the radiative Euler equations, which are a fundamental system in radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena. One of our main motivations is to attempt to explore how nonlinear radiative inhomogeneity influences the behavior of entropy solutions. Simple but different phenomena are observed on relaxation limits. On one hand, the same relaxation limit such as the hyperbolic-hyperbolic type limit is obtained, even for different scaling. On the other hand, different relaxation limits including hyperbolic-hyperbolic type and hyperbolic-parabolic type limits are obtained, even for the same scaling if different conditions are imposed on nonlinear radiative inhomogeneity.

Keywords

Radiating gas model / nonlinear radiative inhomogeneity / entropy solution / global well-posedness / relaxation limit