Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity
文献类型：期刊论文
| 作者 | Jiu, Quansen1,2; Wang, Yi2,3,4 ; Xin, Zhouping2
|
| 刊名 | COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2011 |
| 卷号 | 36期号:4页码:602-634 |
| 关键词 | Density-dependent Navier-Stokes equations Rarefaction wave Stability Weak solution |
| ISSN号 | 0360-5302 |
| DOI | 10.1080/03605302.2010.516785 |
| 英文摘要 | In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is constructed by approximating the system and regularizing the initial values which may contain vacuum states. Then some global in time estimates on the weak solution are obtained. Based on these uniform estimates, the vacuum states are shown to vanish in finite time and the weak solution we constructed becomes a unique strong one. Consequently, the stability of the rarefaction wave is proved in a weak sense. The theory holds for large-amplitudes rarefaction waves and arbitrary initial perturbations. |
| 资助项目 | National Natural Sciences Foundation of China[10871133] ; National Natural Sciences Foundation of China[10801128] ; Beijing Education Committee ; Zheng Ge Ru Funds ; Hong Kong RGC Earmarked Research Grant[CUHK4042/08P] ; Hong Kong RGC Earmarked Research Grant[CUHK4040/06P] ; Chinese University of Hong Kong |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000286522000002 |
| 出版者 | TAYLOR & FRANCIS INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13058]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Jiu, Quansen |
| 作者单位 | 1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China 2.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China 3.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing, Peoples R China 4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Jiu, Quansen,Wang, Yi,Xin, Zhouping. Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2011,36(4):602-634. |
| APA | Jiu, Quansen,Wang, Yi,&Xin, Zhouping.(2011).Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,36(4),602-634. |
| MLA | Jiu, Quansen,et al."Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 36.4(2011):602-634. |
入库方式： OAI收割
来源：数学与系统科学研究院
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