Existence results and blow-up criterion of compressible radiation hydrodynamic equations

2014/07/29 by Yachun li, li, Yachun, Shengguo Zhu +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1407.7830

47pages

arxiv created 2014/11/24 · arxiv updated 2014/11/25

Abstract

In this paper, we consider the 3D compressible radiation hydrodynamic (RHD) equations with thermal conductivity in a bounded domain. The existence of unique local strong solutions is firstly established when the initial data are arbitrarily large and satisfy some initial layer compatibility condition. The initial mass density needs not be bounded away from zero and may vanish in some open set. Moreover, we show that if the initial vacuum domain is not so irregular, then the compatibility condition is necessary and sufficient to guarantee the existence of the unique strong solution. Finally, we show a Beal-Kato-Majda type blow-up criterion in terms of (∇ I,ρ,θ).

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