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arXiv · 1309.7420

On regular solutions of the 3-D compressible isentropic Euler-Boltzmann equations with vacuum

Yachun Li·Shengguo Zhu
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Abstract

In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the theory of quasi-linear symmetric hyperbolic systems under some physical assumptions. Then we give the non-global existence of regular solutions caused by the effect of vacuum for $1<γ\leq 3$. Finally, we extend our result to the initial-boundary value problem under some suitable boundary conditions. These blow-up results tell us that the radiation cannot prevent the formation of singularities caused by the appearance of vacuum.

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Yachun Li, Shengguo Zhu. 2014-10-07. On regular solutions of the 3-D compressible isentropic Euler-Boltzmann equations with vacuum. https://arxiv.org/abs/1309.7420

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