Abstract
We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier-Stokes equations in a bounded domain and a classical (nonlinear) full von Karman plate equations that accounts for both transversal and lateral displacements on a flexible part of the boundary. Rotational inertia of the filaments of the plate is not taken into account. Our main result shows well-posedness of strong solutions to the problem, thus the problem generates a semiflow in an appropriate phase space. We also prove uniform stability of strong solutions to homogeneous problem.
Highlights
We deal with a coupled system which describes an interaction of a homogeneous viscous incompressible fluid which occupies a domain O bounded by the walls of the container S and a horizontal part of the boundary ∂O Ω on which a thin elastic plate is placed
The motion of the fluid is described by linearized 3D Navier–Stokes equations
To achieve existence of strong solutions we prove additional smooth estimates for the first and second derivatives of the components of (1)–(8)
Summary
We deal with a coupled system which describes an interaction of a homogeneous viscous incompressible fluid which occupies a domain O bounded by the (solid) walls of the container S and a horizontal (flat) part of the boundary ∂O Ω on which a thin (nonlinear) elastic plate is placed. The following theorem on existence of weak solutions can be proved the same way, as in [9]. The phase space for strong solutions is in agreement with the domain of the generator of the semigroup in the problem of fluid-structure interaction that encounts for in-plane displacements of the plate only, see formula (22) and Remark 2.3 from [5].
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