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

TL;DR

This paper proves the existence of a global attractor for strong solutions of a coupled fluid-plate system without rotational inertia, describing long-term behavior under small external loads.

Contribution

It establishes the existence of a strong attractor for a coupled Navier-Stokes and von Karman plate system without rotational inertia, extending understanding of long-term dynamics.

Findings

Existence of a strong attractor under small external loads

Long-time dynamics of the coupled system are well-defined

No rotational inertia considered in the model

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.