# American Institute of Mathematical Sciences

May  2018, 23(3): 1243-1265. doi: 10.3934/dcdsb.2018150

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

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

* Corresponding author: Iryna Ryzhkova-Gerasymova

Received  March 2017 Revised  July 2017 Published  May 2018 Early access  February 2018

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.

Citation: Iryna Ryzhkova-Gerasymova. Long time behaviour of strong solutions to interactive fluid-plate system without rotational inertia. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1243-1265. doi: 10.3934/dcdsb.2018150
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