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On the global wellposedness to the 3-D incompressible anisotropic Navier- Stokes equations
Chemin, Jean-Yves; Zhang, Ping
2007-06-01
Source PublicationCOMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN0010-3616
Volume272Issue:2Pages:529-566
AbstractCorresponding to the wellposedness result [2] for the classical 3-D Navier-Stokes equations (NSv) with initial data in the scaling invariant Besov space, beta(-1+ 3/p)(p,infinity) , here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations (ANS(v)), where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, beta(-1/2, 1/2)(4) and beta(-1/2, 1/2)(4) (T). Then with initial data in the scaling invariant space beta(-1/2, 1/2)(4), we prove the global wellposedness for (ANS(v)) provided the norm of initial data is small enough compared to the horizontal viscosity. In particular, this result implies the global wellposedness of (ANS(v)) with high oscillatory initial data (1.2).
DOI10.1007/s00220-007-0236-0
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000247964500007
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/4671
Collection数学所
Corresponding AuthorChemin, Jean-Yves
Affiliation1.Univ Paris 06, Lab JL Lyons, F-75230 Paris 05, France
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Chemin, Jean-Yves,Zhang, Ping. On the global wellposedness to the 3-D incompressible anisotropic Navier- Stokes equations[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2007,272(2):529-566.
APA Chemin, Jean-Yves,&Zhang, Ping.(2007).On the global wellposedness to the 3-D incompressible anisotropic Navier- Stokes equations.COMMUNICATIONS IN MATHEMATICAL PHYSICS,272(2),529-566.
MLA Chemin, Jean-Yves,et al."On the global wellposedness to the 3-D incompressible anisotropic Navier- Stokes equations".COMMUNICATIONS IN MATHEMATICAL PHYSICS 272.2(2007):529-566.
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