Local Existence and Finite-Time Blow-Up in Multidimensional Radiation Hydrodynamics
Xinhua Zhong and Song Jiang
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.