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.
Accepté le :
DOI : 10.1051/cocv/2016032
Keywords: Stokes system, controllability, Lagrangian controllability, Runge theorem
Glass, O. 1 ; Horsin, T. 2
@article{COCV_2016__22_4_1040_0,
author = {Glass, O. and Horsin, T.},
title = {Lagrangian controllability at low {Reynolds} number},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1040--1053},
year = {2016},
publisher = {EDP Sciences},
volume = {22},
number = {4},
doi = {10.1051/cocv/2016032},
mrnumber = {3570493},
zbl = {1388.93020},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016032/}
}
TY - JOUR AU - Glass, O. AU - Horsin, T. TI - Lagrangian controllability at low Reynolds number JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 1040 EP - 1053 VL - 22 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016032/ DO - 10.1051/cocv/2016032 LA - en ID - COCV_2016__22_4_1040_0 ER -
%0 Journal Article %A Glass, O. %A Horsin, T. %T Lagrangian controllability at low Reynolds number %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 1040-1053 %V 22 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016032/ %R 10.1051/cocv/2016032 %G en %F COCV_2016__22_4_1040_0
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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