Global Wellposedness Of Entropy Solution And Relaxation Limits Of The Multi-dimensional Approximate Radiative Euler Equations

We study the Cauchy problem of the multi-dimensional approximate radiative Euler equations.Such equations give good approximation to the radiative Euler e-quations,which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena.One of our motiva-tions is to try to find some suitable conditions on nonlinear radiative inhomogeneity to guarantee to the global-in-time wellposedness of the Cauchy problem.Moreover,after suitable scalings and conditions on nonlinear radiative inhomogeneity,relax-ation limits are also analyzed.In particular,an interesting phenomenon is observed.On one hand,the same relaxation limit such as hyperbolic-hyperbolic type limit is obtained,even for different scaling.On the other hand,different relaxation limits in-cluding hyperbolic-hyperbolic type and hyperbolic-parabolic type limits are obtained,even for the same scaling if different conditions are imposed on nonlinear radiative inhomogeneity.Our investigations on relaxation limits provide further understanding on nonlinear radiative inhomogeneity.