, Volume 9, Issue 4, pp 543-564
Date: 19 Sep 2006

Local Existence and Finite-time Blow-up in Multidimensional Radiation Hydrodynamics

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Abstract.

We first prove the local existence of smooth solutions to the Cauchy problem for the equations of multidimensional radiation hydrodynamics which are a hyperbolic-Boltzmann coupled system. Then, we show that a smooth solution will blow up in finite time if the initial data are large. Moreover, the property of finite propagation speed is obtained simultaneously.

Communicated by M. Padula
Supported by the NSF of Jiangxi Province, the Special Funds for Major State Basic Research Projects, the NSFC (Grant No. 10225105) and the CAEP (Grant No. 2003-R-02).