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Sbornik: Mathematics, 2012, Volume 203, Issue 9, Pages 1244–1268
DOI: https://doi.org/10.1070/SM2012v203n09ABEH004263 (Mi sm7882) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary

A. V. Gorshkov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (406 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM2012v203n09ABEH004263
Abstract: The problem of stabilizing a solution of the 2D Navier-Stokes system defined in the exterior of a bounded domain with smooth boundary is investigated. For a given initial velocity field a control on the boundary of the domain must be constructed such that the solution stabilizes to a prescribed vortex solution or trivial solution at the rate of $1/{t^k}$. On the way, related questions are investigated, concerning the behaviour of the spectrum of an operator under a relatively compact perturbation and the existence of attracting invariant manifolds.
Bibliography: 21 titles.
Keywords: Navier-Stokes system, Lamb-Oseen vortex, stabilization, boundary control, invariant manifolds.
Received: 28.04.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 9, Pages 15–40
DOI: https://doi.org/10.4213/sm7882
Bibliographic databases:
Document Type: Article
UDC: 517.956.45
MSC: Primary 93C20, 35Q30; Secondary 93D15
Language: English
Original paper language: Russian
Citation: A. V. Gorshkov, “Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary”, Mat. Sb., 203:9 (2012), 15–40; Sb. Math., 203:9 (2012), 1244–1268
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:649
    Russian version PDF:253
    English version PDF:5
    References:64
    First page:38
     
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