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

Abstract

This paper is devoted to a long-time behavior analysis of flow-structure interactions at subsonic and supersonic velocities. An intrinsic component of that analysis is the study of attractors corresponding to von Karman plate equations with delayed terms and without rotational terms. The presence of delay terms in the dynamical system leads to a loss of gradient structure, while the absence of rotational terms in von Karman plates leads to the loss of compactness of the orbits. Both of these features make the analysis of long-time behavior rather subtle, rendering the established tools in the theory of PDE and dynamical systems not applicable. We develop methodology that is capable of addressing this class of problems.