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Lagrangian controllability at low Reynolds number

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 28 Jul 2016Embargo end date: 01 Jan 2016 France Publisher:EDP SciencesJournal:ESAIM: Control, Optimisation and Calculus of Variations, volume 22, pages 1,040-1,053 (issn: 1292-8119, eissn: 1262-3377,

Authors: Glass, Olivier; Horsin, Thierry;

doi: 10.1051/cocv/2016032 , 10.48550/arxiv.1602.03045

arXiv: http://arxiv.org/abs/1602.03045

Lagrangian controllability at low Reynolds number

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Abstract

In this paper, we establish a result of Lagrangian controllability for a fluid at low Reynolds number, driven by the stationary Stokes equation. This amounts to the possibility of displacing a part of a fluid from one zone to another by suitably using a boundary control. This relies on a weak variant of the Runge-Walsh's theorem (on approximation of harmonic functions) concerning the Stokes equation. We give two variants of this result, one of which we believe to be better adapted to numerical simulations.

Country

France

Related Organizations

PSL Research University
France
Centre De Recherche en Mathématiques de la Décision
France
Conservatoire national des arts et métiers
France
Conservatoire national des arts et métiers
France
Paris Dauphine University
France

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Keywords

Stokes system, [MATH] Mathematics [math], Analyse, controllability, 510, 620, Runge theorem, Mathematics - Analysis of PDEs, 515, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Optimization and Control, Lagrangian controllability, Analysis of PDEs (math.AP)

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