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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 shallow shell equations that accounts for both transversal and lateral displacements on a flexible part of the boundary. We also take into account rotational inertia of filaments of the shell. Out main result shows that the problem generates a semiflow in an appropriate phase space. The regularity provided by viscous dissipation in the fluid allows us to consider simultaneously both cases of presence inertia in the lateral displacements and its absence. Our second result states the existence of a compact global attractor for this semiflow in the case of presence of (rotational) damping in the transversal component and a particular structure of external forces.

    [**Keywords:** ]{} Fluid–structure interaction, linearized 3D Navier–Stokes equations, nonlinear shell, global attractor.

    [**2010 MSC:**]{} 74F10, 35B41, 35Q30, 74K20
author:
- |
    Igor Chueshov[^1]     and     Iryna Ryzhkova[^2]\
    \
    Department of Mechanics and Mathematics,\
    Kharkov National University,\
    Kharkov, 61077, Ukraine\
title:  Unsteady interaction of a viscous fluid with an elastic shell modeled by full von Karman equations
---

Introduction
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We consider a coupled (hybrid) system which describes 