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Some remarks about the possible blow-up for the Navier-Stokes equations
Chemin, Jean-Yves1; Gallagher, Isabelle2,3; Zhang, Ping4,5,6
2019-07-17
Source PublicationCOMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN0360-5302
Pages19
AbstractIn this work, we investigate the question of preventing the three-dimensional, incompressible Navier-Stokes equations from developing singularities, by controlling one component of the velocity field only, in space-time scale invariant norms. In particular we prove that it is not possible for one component of the velocity field to tend to 0 too fast near blow up. We also introduce a space "almost" invariant under the action of the scaling such that if one component of the velocity field measured in this space remains small enough, then there is no blow up.
KeywordAnisotropic Littlewood-Paley Theory blow-up criteria incompressible Navier-Stokes equations
DOI10.1080/03605302.2019.1641725
Language英语
Funding ProjectNSF of China[11371347] ; NSF of China[11688101] ; National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000476300200001
PublisherTAYLOR & FRANCIS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35212
Collection数学所
Corresponding AuthorZhang, Ping
Affiliation1.Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, Paris 05, France
2.PSL Res Univ, CNRS, Ecole Normale Super, DMA, Paris, France
3.Univ Paris Diderot, Sorbonne Paris Cite, UFR Math, Paris, France
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
5.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China
6.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Chemin, Jean-Yves,Gallagher, Isabelle,Zhang, Ping. Some remarks about the possible blow-up for the Navier-Stokes equations[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2019:19.
APA Chemin, Jean-Yves,Gallagher, Isabelle,&Zhang, Ping.(2019).Some remarks about the possible blow-up for the Navier-Stokes equations.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,19.
MLA Chemin, Jean-Yves,et al."Some remarks about the possible blow-up for the Navier-Stokes equations".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2019):19.
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