On the Decay and Stability of Global Solutions to the 3D Inhomogeneous Navier-Stokes Equations

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	On the Decay and Stability of Global Solutions to the 3D Inhomogeneous Navier-Stokes Equations
	Abidi, Hammadi 1; Gui, Guilong 2; Zhang, Ping3,4
	2011-06-01
发表期刊	COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN	0010-3640
卷号	64 期号:6 页码:832-881
摘要	In 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.
语种	英语
资助项目	NSF of China[10421101] ; NSF of China[10931007] ; NSF of China[11001111] ; 973 Program[2006CB805902] ; Chinese Academy of Sciences[GJHZ2-00829]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000288178500003
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12828
专题	数学所
通讯作者	Abidi, Hammadi
作者单位	1.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
推荐引用方式 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.