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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
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).
Rights and permissions
About this article
Cite this article
Zhong, X., Jiang, S. Local Existence and Finite-time Blow-up in Multidimensional Radiation Hydrodynamics. J. math. fluid mech. 9, 543–564 (2007). https://doi.org/10.1007/s00021-005-0213-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00021-005-0213-3