Interaction of an elastic plate    with a linearized inviscid incompressible  fluid

I. D. Chueshov

doi:10.3934/cpaa.2014.13.1759

Article Contents

2014, Volume 13, Issue 5: 1759-1778. Doi: 10.3934/cpaa.2014.13.1759

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Interaction of an elastic plate with a linearized inviscid incompressible fluid

I. D. Chueshov^1,

1.
Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov

Received: May 31, 2013

Revised: August 31, 2013

Published: August 2015

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Abstract

We prove well-posedness of energy type solutions to an interacting system consisting of the 3D linearized Euler equations and a (possibly nonlinear) elastic plate equation describing large deflections of a flexible part of the boundary. In the damped case under some conditions concerning the plate nonlinearity we prove the existence of a compact global attractor for the corresponding dynamical system and describe the situations when this attractor has a finite fractal dimension.

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Mathematics Subject Classification: Primary: 74F10; Secondary: 35B41, 35Q30, 74K20.

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