Feedback stabilization of the incompressible Navier-Stokes equations coupled with a damped elastic system in two dimensions. (English) Zbl 1386.93153
Summary: 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.
MSC:
| 93C20 | Control/observation systems governed by partial differential equations |
| 93B52 | Feedback control |
| 93D15 | Stabilization of systems by feedback |
| 35Q30 | Navier-Stokes equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
Keywords:
fluid-structure interaction; feedback control; stabilization; Navier-Stokes equations; damped elastic systemReferences:
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