Smooth Controllability of the Navier-Stokes Equation with Navier Conditions: Application to Lagrangian Controllability
文献类型：期刊论文
| 作者 | Liao, Jiajiang1,2; Sueur, Franck3,4; Zhang, Ping2,5,6 |
| 刊名 | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
 |
| 出版日期 | 2022-02-01 |
| 卷号 | 243期号:2页码:869-941 |
| ISSN号 | 0003-9527 |
| DOI | 10.1007/s00205-021-01744-2 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000740214000001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59832]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。