Attractors for Delayed, Non-Rotational von Karman Plates with Applications to Flow-Structure Interactions Without any Damping

TL;DR

This paper investigates the long-term behavior of flow-structure interactions involving von Karman plates with delays and no rotational effects, developing new methods to analyze their complex dynamics.

Contribution

It introduces novel analytical techniques to study attractors in delayed, non-rotational von Karman plate models where traditional PDE dynamical system tools fail.

Findings

Identification of attracting sets in complex flow-structure models

Development of new methods for non-gradient, non-compact PDE systems

Insights into long-term dynamics of delayed flow-plate interactions

Abstract

This paper is devoted to a long time behavior analysis associated with flow structure interactions at subsonic and supersonic velocities. It turns out that an ntrinsic component of that analysis is the study of attracting sets corresponding to von Karman plate equations with {\it delayed terms} and {\it without rotational} terms. The presence of delay terms in the dynamical system leads to the loss of gradient structure while the absence of rotational terms in von Karman plates leads to the loss of compactness of the orbits. Both these features make the analysis of long time behavior rather subtle rendering the established tools in the theory of PDE dynamical systems not applicable. It is our goal to develop methodology that is capable of handling this class of problems.