Local Existence Of Strong Solutions To The Cauchy Problem Of Compressible Radiation Hydrodynamics Equations With Vacuum

In this paper we consider the3-D compressible isentropic radiation hydrodynam-ics (RHD) equations. Radiation hydrodynamics theory has a wide range of applica-tions, such as in astrophysics, laser fusion, supernova explosions, etc. Based on thelocal existence of strong solutions when viscosity coefcients are constants[18], weconsider the case when bulk viscosity coefcient relies on the mass density. The maincontent of this paper is:1. The local existence of strong solutions to the Cauchy problem of isentropicNavier-Stokes-Boltzmann Equations is frstly established through a priori estimate andPicard Iteration method when the initial data contain vacuum and satisfy some initiallayer compatibility condition.2. Wealsoprovethatiftheinitialvacuumisnotsoirregular,thenthecompatibilitycondition of the initial data is necessary and sufcient to guarantee the existence of aunique strong solution.