Journal of Mathematical Fluid Mechanics

, Volume 19, Issue 4, pp 773–805

# Feedback Stabilization of the Incompressible Navier–Stokes Equations Coupled with a Damped Elastic System in Two Dimensions

• Debayan Maity
• Jean-Pierre Raymond
Article

## Abstract

In this article we study a system coupling the incompressible Navier–Stokes equations with an elastic structure governed by a damped wave equation in a two dimensional channel with periodic boundary conditions. The elastic structure is located at the upper boundary of the domain occupied by the fluid. The domain occupied by the fluid depends on the displacement of the elastic structure, and therefore it depends on time. We prove that this coupled system may be stabilized around the steady state zero, at any exponential decay rate, by a Dirichlet control acting in the lower boundary of the fluid domain.

## Keywords

Fluid-structure interaction feedback control stabilization Navier–Stokes equations damped elastic system

## Mathematics Subject Classification

93C20 93B52 93D15 35Q30 76D05 74F10

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