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Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable
Gui, Guilong3; Huang, Jingchi1; Zhang, Ping1,2
2011-12-01
Source PublicationJOURNAL OF FUNCTIONAL ANALYSIS
ISSN0022-1236
Volume261Issue:11Pages:3181-3210
AbstractMotivated 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.
KeywordInhomogeneous Navier-Stokes systems Anisotropic Littlewood-Paley theory Large solutions
DOI10.1016/j.jfa.2011.07.026
Language英语
Funding ProjectNSF of China[11001111] ; NSF of China[10421101] ; NSF of China[10931007] ; Jiangsu University[10JDG141] ; Jiangsu University[10JDG157] ; Chinese Academy of Sciences[GJHZ200829]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000295439100003
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12323
Collection数学所
Corresponding AuthorZhang, Ping
Affiliation1.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
Recommended Citation
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.
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