On the global wellposedness to the 3-D incompressible anisotropic Navier- Stokes equations

doi:10.1007/s00220-007-0236-0

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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
发表期刊	COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN	0010-3616
卷号	272 期号:2 页码:529-566
摘要	Corresponding 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).
DOI	10.1007/s00220-007-0236-0
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000247964500007
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4671
专题	数学所
通讯作者	Chemin, Jean-Yves
作者单位	1.Univ Paris 06, Lab JL Lyons, F-75230 Paris 05, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 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.