The aim of this work is to show the local null controllability of a fluid–solid interaction system by using a distributed control located in the fluid. The fluid is modeled by the incompressible Navier–Stokes system with Navier slip boundary conditions and the rigid body is governed by the Newton laws. Our main result yields that we can drive the velocities of the fluid and of the structure to 0 and we can control exactly the position of the rigid body. One important ingredient consists in a new Carleman estimate for a linear fluid–rigid body system with Navier boundary conditions. This work is done without imposing any geometrical conditions on the rigid body.
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Keywords: Navier–Stokes system, Navier slip boundary conditions, Null controllability, fluid–solid interaction system
@article{COCV_2021__27_1_A78_0,
author = {Djebour, Imene Aicha},
title = {Local null controllability of a fluid{\textendash}rigid body interaction problem with {Navier} slip boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021071},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021071/}
}
TY - JOUR AU - Djebour, Imene Aicha TI - Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021071/ DO - 10.1051/cocv/2021071 LA - en ID - COCV_2021__27_1_A78_0 ER -
%0 Journal Article %A Djebour, Imene Aicha %T Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021071/ %R 10.1051/cocv/2021071 %G en %F COCV_2021__27_1_A78_0
Djebour, Imene Aicha. Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 76. doi: 10.1051/cocv/2021071
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