Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

doi:10.1007/s00220-011-1350-6

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	Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces
	Paicu, Marius 1; Zhang, Ping2,3
	2011-11-01
发表期刊	COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN	0010-3616
卷号	307 期号:3 页码:713-759
摘要	In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B and B-4(-1/2, 1/2) (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS(nu)) has a unique global solution with initial data u(0) = (u(0)(h), u(0)(3)) which satisfies parallel to u(0)(h)parallel to B exp(C/nu(4) parallel to u(0)(3)parallel to(4)(B)) <= c(0)nu or parallel to u(0)(h)parallel to(B4-1/2, 1/2) exp(C/nu(4)parallel to u(0)(3)parallel to(4)(B4-1/2, 1/2)) <= c(0)nu for some c(0) sufficiently small. To overcome the difficulty that Gronwall's inequality can not be applied in the framework of Chemin-Lerner type spaces, <(L-t(p))over tilde>(B), we introduced here sort of weighted Chemin-Lerner type spaces, <(L-t, f(2))over tilde>(B) for some apropriate L-1 function f(t).
DOI	10.1007/s00220-011-1350-6
语种	英语
资助项目	NSF of China[10421101] ; NSF of China[10931007] ; Chinese Academy of Sciences[GJHZ200829]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000296651900005
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/12941
专题	数学所
通讯作者	Paicu, Marius
作者单位	1.Univ Bordeaux 1, Inst Math Bordeaux, F-33405 Talence, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Paicu, Marius,Zhang, Ping. Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2011,307(3):713-759.
APA	Paicu, Marius,&Zhang, Ping.(2011).Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces.COMMUNICATIONS IN MATHEMATICAL PHYSICS,307(3),713-759.
MLA	Paicu, Marius,et al."Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces".COMMUNICATIONS IN MATHEMATICAL PHYSICS 307.3(2011):713-759.