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: email@example.com
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
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