Global existence of strong solutions to the Cauchy problem for a 1D radiative gas

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:346

Article

Wang, Jing³  Xie, Feng^1,2 

[1] Inst Appl Phys & Computat Math, LCP, Beijing 100088, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[3] CUHK, Inst Math Sci, Shatin, Hong Kong, Peoples R China

关键词: compressible radiation hydrodynamics;    equilibrium diffusion approximation;    Cauchy problem;    global strong solutions;    large initial data;   

DOI  :  10.1016/j.jmaa.2008.05.066

来源: Elsevier

【 摘 要 】

We consider a one-dimensional radiation hydrodynamics model in the case of the equilibrium diffusion approximation which is described by the compressible Navier-Stokes system with the additional terms in the pressure and internal energy respectively, which embody the effect of radiation. Under the physical growth conditions on the heat conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy problem with large initial data, where the initial density and velocity may have differing constant states at infinity. Moreover, we show that if there is no vacuum ill the initial density, then, the vacuum and concentration of the density will never occur in any finite time. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free