Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Li, Yachun^1,2  Zhu, Shengguo^1,3 

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

[2] Shanghai Jiao Tong Univ, Key Lab Sci & Engn Comp MOE, Shanghai 200240, Peoples R China

[3] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: Navier-Stokes-Boltzmann equations;    Classical solutions;    Vacuum;    Blow-up;   

DOI  :  10.1016/j.jde.2014.03.007

来源: Elsevier

【 摘 要 】

We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multidimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as for one-dimensional case. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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