Geodesic
Lagrangian controllability at low Reynolds number
Glass, O.1  ; Horsin, T.2 
1 CEREMADE, Université Paris-Dauphine & CNRS, PSL, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France.
2 Conservatoire National des Arts et Métiers, M2N, Case 2D 5000, 292 rue Saint-Martin, 75003 Paris, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1040-1053

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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.

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DOI : 10.1051/cocv/2016032
Classification : 76D07, 76D55, 35Q30, 34H05, 93B05, 35A35
Keywords: Stokes system, controllability, Lagrangian controllability, Runge theorem

Glass, O. 1 ; Horsin, T. 2

1 CEREMADE, Université Paris-Dauphine & CNRS, PSL, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France.
2 Conservatoire National des Arts et Métiers, M2N, Case 2D 5000, 292 rue Saint-Martin, 75003 Paris, France. 
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     title = {Lagrangian controllability at low {Reynolds} number},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1040--1053},
     publisher = {EDP-Sciences},
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Glass, O.; Horsin, T. Lagrangian controllability at low Reynolds number. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1040-1053. doi: 10.1051/cocv/2016032

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