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Global Controllability of the Navier-Stokes Equations in the Presence of Curved Boundary with No-Slip Conditions
Liao, Jiajiang1; Sueur, Franck2,3; Zhang, Ping4,5
2022-08-01
Source PublicationJOURNAL OF MATHEMATICAL FLUID MECHANICS
ISSN1422-6928
Volume24Issue:3Pages:32
AbstractWe consider the issue of the small-time global exact null controllability of the axi-symmetric incompressible Navier-Stokes equation in a 3D finite vertical cylinder with circular section. We assume that we are able to act on the fluid flow on the top and on the bottom of the cylinder while no-slip conditions are prescribed on the boundary of the lateral section. We also make use of a distributed control, which can be chosen arbitrarily small for any Sobolev regularity in space. Our work improves earlier results in Guerrero et al. (C R Math Acad Sci Paris 343:573-577, 2006; J Math Pures Appl (9) 98:689-709, 2012) where the distributed force is small only in a negative Sobolev space and the recent work Coron et al. (Ann PDE 5(2):1-49, 2019) where the case of the 2D incompressible Navier-Stokes equation in a rectangle was considered. Our analysis actually follows quite narrowly the one in Coron et al. (2019) by making use of Coron's return method, of the well-prepared dissipation method and of long-time nonlinear Cauchy-Kovalevskaya estimates. An extra difficulty here is the curvature of the uncontrolled part of the boundary which requires further analysis to apply the well-prepared dissipation method to lower order boundary layer terms.
KeywordAxi-symmetric Navier-Stokes equations Controllability No-slip Dirichlet boundary condition Boundary layers Return method Multi-scales asymptotic expansion Well-prepared dissipation method Long-time nonlinear Cauchy-Kovalevskaya estimates
DOI10.1007/s00021-022-00689-0
Indexed BySCI
Language英语
Funding ProjectK. C. Wong Education Foundation ; Agence Nationale de la Recherche[ANR-18-CE40-0027-01] ; National Science Foundation[DMS-1928930] ; National Key R &D Program of China[2021YFA1000800] ; NSF of China[11731007] ; NSF of China[12031006] ; NSF of China[11688101]
WOS Research AreaMathematics ; Mechanics ; Physics
WOS SubjectMathematics, Applied ; Mechanics ; Physics, Fluids & Plasmas
WOS IDWOS:000806792900001
PublisherSPRINGER BASEL AG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61476
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLiao, Jiajiang
Affiliation1.Inst Appl Phys & Computat Math, Beijing 100188, Peoples R China
2.Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France
3.Inst Univ France, Paris, France
4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Liao, Jiajiang,Sueur, Franck,Zhang, Ping. Global Controllability of the Navier-Stokes Equations in the Presence of Curved Boundary with No-Slip Conditions[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS,2022,24(3):32.
APA Liao, Jiajiang,Sueur, Franck,&Zhang, Ping.(2022).Global Controllability of the Navier-Stokes Equations in the Presence of Curved Boundary with No-Slip Conditions.JOURNAL OF MATHEMATICAL FLUID MECHANICS,24(3),32.
MLA Liao, Jiajiang,et al."Global Controllability of the Navier-Stokes Equations in the Presence of Curved Boundary with No-Slip Conditions".JOURNAL OF MATHEMATICAL FLUID MECHANICS 24.3(2022):32.
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