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

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https://www.aimsciences.org/en/article/doi/10.3934/dcdss.2014.7.925

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https://doi.org/10.3934/dcdss.2014.7.925
 http://hdl.handle.net/11603/34625

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0002-2443-3789

Date

2014-10

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journal articles
preprints
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Citation of Original Publication

Chueshov, Igor, Irena Lasiecka, and Justin Webster. "Flow-Plate Interactions: Well-Posedness and Long-Time Behavior." Discrete and Continuous Dynamical Systems - S 7, no. 5 (May 1, 2014): 925–65. https://doi.org/10.3934/dcdss.2014.7.925.

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This is the version of the article before peer review or editing, as submitted by an author to Flow-plate interactions: Well-posedness and long-time behavior https://www.aimsciences.org/article/doi/10.3934/dcdss.2014.7.925. AIMS is not responsible for any errors or omissions in this version of the manuscript, or any version derived from it.

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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 resultson existence, uniqueness, and stability of weak solutions, (ii) to present a construction of finite dimensional, attracting setscorresponding 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 aPDE system with delay.