In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time . Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.
Mots-clés : Navier-Stokes system, controllability, slip
@article{COCV_2006__12_3_484_0,
author = {Guerrero, Sergio},
title = {Local exact controllability to the trajectories of the {Navier-Stokes} system with nonlinear {Navier-slip} boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {484--544},
publisher = {EDP-Sciences},
volume = {12},
number = {3},
year = {2006},
doi = {10.1051/cocv:2006006},
mrnumber = {2224824},
zbl = {1106.93011},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2006006/}
}
TY - JOUR AU - Guerrero, Sergio TI - Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 484 EP - 544 VL - 12 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2006006/ DO - 10.1051/cocv:2006006 LA - en ID - COCV_2006__12_3_484_0 ER -
%0 Journal Article %A Guerrero, Sergio %T Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 484-544 %V 12 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2006006/ %R 10.1051/cocv:2006006 %G en %F COCV_2006__12_3_484_0
Guerrero, Sergio. Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 484-544. doi : 10.1051/cocv:2006006. http://www.numdam.org/articles/10.1051/cocv:2006006/
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