Local well‐posedness of compressible radiation hydrodynamic equations with density‐dependent viscosities and vacuum

Abstract

In this paper, we consider the Cauchy problem for three‐dimensional isentropic compressible radiation hydrodynamic equations with density‐dependent viscosity coefficients. When the viscosity coefficients are given as power of density (ρδ with δ > 1), we establish the local‐in‐time existence of classical solutions containing a vacuum for large initial data. Here, we point out that the initial layer compatibility conditions are not necessary.