| Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable | |
Gui, Guilong3; Huang, Jingchi1; Zhang, Ping1,2
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| 2011-12-01 | |
| Source Publication | JOURNAL OF FUNCTIONAL ANALYSIS
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| ISSN | 0022-1236 |
| Volume | 261Issue:11Pages:3181-3210 |
| Abstract | 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. |
| Keyword | Inhomogeneous Navier-Stokes systems Anisotropic Littlewood-Paley theory Large solutions |
| DOI | 10.1016/j.jfa.2011.07.026 |
| Language | 英语 |
| Funding Project | NSF of China[11001111] ; NSF of China[10421101] ; NSF of China[10931007] ; Jiangsu University[10JDG141] ; Jiangsu University[10JDG157] ; Chinese Academy of Sciences[GJHZ200829] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000295439100003 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/12323 |
| Collection | 数学所 |
| Corresponding Author | Zhang, Ping |
| Affiliation | 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 |
| 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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