Long time behaviour of strong solutions to interactive fluid-plate system without rotational inertia

Iryna Ryzhkova-Gerasymova

doi:10.3934/dcdsb.2018150

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2018, Volume 23, Issue 3: 1243-1265. Doi: 10.3934/dcdsb.2018150

This issue Previous Article On the Oseledets-splitting for infinite-dimensional random dynamical systems Next Article Semigroup well-posedness of a linearized, compressible fluid with an elastic boundary

Long time behaviour of strong solutions to interactive fluid-plate system without rotational inertia

Iryna Ryzhkova-Gerasymova^1, ,

1.
V.N.Karazin Karkiv national university, Svobody sq. 4, Kharkiv, 61077, Ukraine

* Corresponding author: Iryna Ryzhkova-Gerasymova
* Corresponding author: Iryna Ryzhkova-Gerasymova

Received: February 28, 2017

Revised: June 30, 2017

Early access: February 2018

Published: June 2018

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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.

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Mathematics Subject Classification: Primary: 35B40, 35D35; Secondary: 35Q35, 35Q74.

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