Lagrangian controllability at low Reynolds number
Glass, Olivier; Horsin, Thierry (2016), Lagrangian controllability at low Reynolds number, ESAIM: Control, Optimisation and Calculus of Variations, 22, 4, p. 1040 - 1053. 10.1051/cocv/2016032
TypeArticle accepté pour publication ou publié
Journal nameESAIM: Control, Optimisation and Calculus of Variations
1040 - 1053
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Abstract (EN)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.
Subjects / KeywordsStokes system; controllability; Lagrangian controllability; Runge theorem
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