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Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces
Paicu, Marius1; Zhang, Ping2,3
2011-11-01
Source PublicationCOMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN0010-3616
Volume307Issue:3Pages:713-759
AbstractIn 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).
DOI10.1007/s00220-011-1350-6
Language英语
Funding ProjectNSF of China[10421101] ; NSF of China[10931007] ; Chinese Academy of Sciences[GJHZ200829]
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000296651900005
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12941
Collection数学所
Corresponding AuthorPaicu, Marius
Affiliation1.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
Recommended Citation
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.
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