Smooth Controllability of the Navier-Stokes Equation with Navier Conditions: Application to Lagrangian Controllability

doi:10.1007/s00205-021-01744-2

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	Smooth Controllability of the Navier-Stokes Equation with Navier Conditions: Application to Lagrangian Controllability
	Liao, Jiajiang 1,2; Sueur, Franck 3,4; Zhang, Ping 2,5,6
	2022-02-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	243 期号:2 页码:869-941
摘要	We deal with the 3D Navier-Stokes equation in a smooth simply connected bounded domain, with controls on a non-empty open part of the boundary and a Navier slip-with-friction boundary condition on the remaining, uncontrolled, part of the boundary. We extend the small-time global exact null controllability result in Coron et al. (J Eur Math Soc 22:1625-1673, 2020) from Leray weak solutions to the case of smooth solutions. Our strategy relies on a refinement of the method of well-prepared dissipation of the viscous boundary layers which appear near the uncontrolled part of the boundary, which allows to handle the multi-scale features in a finer topology. As a byproduct of our analysis we also obtain a small-time global approximate Lagrangian controllability result, extending to the case of the Navier-Stokes equations the recent results (Glass and Horsin in J Math Pures Appl (9) 93:61-90, 2010; Glass and Horsin in SIAM J Control Optim 50: 2726-2742, 2012; Horsin and Kavian in ESAIM Control Optim Calc Var 23:1179-1200, 2017) in the case of the Euler equations and the result (Glass and Horsin in ESAIM Control Optim Calc Var 22:1040-1053, 2016) in the case of the steady Stokes equations.
DOI	10.1007/s00205-021-01744-2
收录类别	SCI
语种	英语
资助项目	K. C. Wong Education Foundation ; Agence Nationale de la Recherche[ANR-15-CE40-0010] ; Agence Nationale de la Recherche[ANR-18-CE40-0027-01] ; Agence Nationale de la Recherche[ANR-16-CE40-0027-01] ; H2020-MSCA-ITN-2017 program, Project ConFlex[ETN-765579] ; NSF of China[11731007] ; NSF of China[12031006] ; NSF of China[11688101]
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000740214000001
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/59833
专题	中国科学院数学与系统科学研究院
通讯作者	Liao, Jiajiang
作者单位	1.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France 4.Inst Univ France, 1 Rue Descartes, F-75231 Paris 05, France 5.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 6.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Liao, Jiajiang,Sueur, Franck,Zhang, Ping. Smooth Controllability of the Navier-Stokes Equation with Navier Conditions: Application to Lagrangian Controllability[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2022,243(2):869-941.
APA	Liao, Jiajiang,Sueur, Franck,&Zhang, Ping.(2022).Smooth Controllability of the Navier-Stokes Equation with Navier Conditions: Application to Lagrangian Controllability.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,243(2),869-941.
MLA	Liao, Jiajiang,et al."Smooth Controllability of the Navier-Stokes Equation with Navier Conditions: Application to Lagrangian Controllability".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 243.2(2022):869-941.