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