Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|Number of page(s)||30|
|Published online||24 June 2021|
Feedback stabilization of a 3D fluid flow by shape deformations of an obstacle*
Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Paul Sabatier,
Toulouse Cedex 9, France.
2 Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India.
** Corresponding author: firstname.lastname@example.org
Accepted: 31 May 2021
We consider a fluid flow in a time dependent domain Ωf(t)=Ω\Ωs(t)̅⊂ℝ3, surrounding a deformable obstacle Ωs(t). We assume that the fluid flow satisfies the incompressible Navier-Stokes equations in Ωf(t), t > 0. We prove that, for any arbitrary exponential decay rate ω > 0, if the initial condition of the fluid flow is small enough in some norm, the deformation of the boundary ∂Ωs(t) can be chosen so that the fluid flow is stabilized to rest, and the obstacle to its initial shape and its initial location, with the exponential decay rate ω > 0.
Mathematics Subject Classification: 93B52 / 93C20 / 93D15 / 35Q30 / 76D55 / 76D05 / 74F10
Key words: Deformable boundary / feedback control / stabilization / Navier-Stokes equations
© 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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.