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Journal of Mathematical Fluid Mechanics

, Volume 9, Issue 4, pp 543–564 | Cite as

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

  • Xinhua ZhongEmail author
  • Song Jiang
Article

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.

Mathematics Subject Classification (2000).

Primary 76-02 Secondary 76N15, 76N10, 35L45, 35L65, 76X05, 35Q35 

Keywords.

Radiation hydrodynamics multidimensions local existence finite-time blow-up finite propagation speed 

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Copyright information

© Birkhaueser 2006

Authors and Affiliations

  1. 1.Department of Basic CoursesBeijing Information Technology InstituteBeijingChina
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingChina

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