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Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity
Jiu, Quansen1,2; Wang, Yi2,3,4; Xin, Zhouping2
2011
Source PublicationCOMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN0360-5302
Volume36Issue:4Pages:602-634
AbstractIn 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.
KeywordDensity-dependent Navier-Stokes equations Rarefaction wave Stability Weak solution
DOI10.1080/03605302.2010.516785
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000286522000002
PublisherTAYLOR & FRANCIS INC
Citation statistics
Cited Times:39[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13059
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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