On an attractor for strong solutions to interactive fluid-plate system without rotational inertia

Abstract

We study long-time dynamics of strong solutions to a non-homogeneous coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) full von Karman plate equations that account 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 is the existence of an attractor in the strong phase space provided lateral external loads are small enough.