Volume 27, 2021
|Number of page(s)||46|
|Published online||13 July 2021|
Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions
Université de Lorraine, CNRS, Inria, IECL,
* Corresponding author: email@example.com
Accepted: 24 June 2021
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.
Mathematics Subject Classification: 35Q30 / 93C20 / 93B05
Key words: Navier–Stokes system / Navier slip boundary conditions / Null controllability / fluid–solid interaction system
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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