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On the Decay and Stability of Global Solutions to the 3D Inhomogeneous Navier-Stokes Equations
Abidi, Hammadi1; Gui, Guilong2; Zhang, Ping3,4
2011-06-01
Source PublicationCOMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN0010-3640
Volume64Issue:6Pages:832-881
AbstractIn this paper, we investigate the large-time decay and stability to any given global smooth solutions of the 3D incompressible inhomogeneous Navier-Stokes equations. In particular, we prove that given any global smooth solution (a, u) of (1.2), the velocity field u decays to 0 with an explicit rate, which coincides with the L(2) norm decay for the weak solutions of the 3D classical Navier-Stokes system [a, u] as t goes to infinity. Moreover, a small perturbation to the initial data of (a, u) still generates a unique global smooth solution to (1.2), and this solution keeps close to the reference solution (a, u) for t > 0. We should point out that the main results in this paper work for large solutions of (1.2). (C) 2010 Wiley Periodicals, Inc.
Language英语
Funding ProjectNSF of China[10421101] ; NSF of China[10931007] ; NSF of China[11001111] ; 973 Program[2006CB805902] ; Chinese Academy of Sciences[GJHZ2-00829]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000288178500003
PublisherWILEY-BLACKWELL
Citation statistics
Cited Times:46[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12828
Collection数学所
Affiliation1.Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Abidi, Hammadi,Gui, Guilong,Zhang, Ping. On the Decay and Stability of Global Solutions to the 3D Inhomogeneous Navier-Stokes Equations[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,2011,64(6):832-881.
APA Abidi, Hammadi,Gui, Guilong,&Zhang, Ping.(2011).On the Decay and Stability of Global Solutions to the 3D Inhomogeneous Navier-Stokes Equations.COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,64(6),832-881.
MLA Abidi, Hammadi,et al."On the Decay and Stability of Global Solutions to the 3D Inhomogeneous Navier-Stokes Equations".COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 64.6(2011):832-881.
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