Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable

doi:10.1016/j.jfa.2011.07.026

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	Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable
	Gui, Guilong 3; Huang, Jingchi 1; Zhang, Ping1,2
	2011-12-01
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	261 期号:11 页码:3181-3210
摘要	Motivated by Chemin and Gallagher (2010) [8], we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier Stokes equations with large initial velocity slowly varying in one space variable. In particular, we proved that when the initial. density is close enough to a positive constant, then given divergence free initial velocity field of the type (v(0)(h) + is an element of w(0)(h) , w(0)(3))(x(h), is an element of x(3)), as that in Chemin and Gallagher (2010) [8] for the classical Navier Stokes system, we shall prove the global wellposedness of (INS) for E sufficiently small. The main difficulty here lies in the fact that we will have to obtain the L-1 (R+; Lip(R-3)) estimate for convection velocity in the transport equation of (INS). Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic type Besov spaces here. (C) 2011 Elsevier Inc. All rights reserved.
关键词	Inhomogeneous Navier-Stokes systems Anisotropic Littlewood-Paley theory Large solutions
DOI	10.1016/j.jfa.2011.07.026
语种	英语
资助项目	NSF of China[11001111] ; NSF of China[10421101] ; NSF of China[10931007] ; Jiangsu University[10JDG141] ; Jiangsu University[10JDG157] ; Chinese Academy of Sciences[GJHZ200829]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000295439100003
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12323
专题	数学所
通讯作者	Zhang, Ping
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 3.Jiangsu Univ, Dept Math, Zhenjiang 212013, Peoples R China
推荐引用方式 GB/T 7714	Gui, Guilong,Huang, Jingchi,Zhang, Ping. Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2011,261(11):3181-3210.
APA	Gui, Guilong,Huang, Jingchi,&Zhang, Ping.(2011).Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable.JOURNAL OF FUNCTIONAL ANALYSIS,261(11),3181-3210.
MLA	Gui, Guilong,et al."Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable".JOURNAL OF FUNCTIONAL ANALYSIS 261.11(2011):3181-3210.