Flow-plate interactions: Well-posedness and long-time behavior

Igor Chueshov; Irena Lasiecka; Justin Webster

doi:10.3934/dcdss.2014.7.925

Article Contents

2014, Volume 7, Issue 5: 925-965. Doi: 10.3934/dcdss.2014.7.925

This issue Previous Article Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model Next Article Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions

Flow-plate interactions: Well-posedness and long-time behavior

1.
Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov
2.
University of Memphis, Department of Mathematical Sciences, 373 Dunn Hall, Memphis, TN 38152
3.
Oregon State University, Department of Mathematics, 368 Kidder Hall, Corvallis, OR 97330

Received: February 28, 2013

Revised: May 31, 2013

Published: September 2014

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Abstract

We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment of the so called Kutta-Joukowsky flow conditions are given in the subsonic case. The goal of the paper is threefold: (i) to provide an accurate review of recent results on existence, uniqueness, and stability of weak solutions, (ii) to present a construction of finite dimensional, attracting sets corresponding to the structural dynamics and discuss convergence of trajectories, and (iii) to state several open questions associated with the topic. This second task is based on a decoupling technique which reduces the analysis of the full flow-structure system to a PDE system with delay.

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Mathematics Subject Classification: Primary: 35M33, 74F10; Secondary: 35B41, 35Q74.

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