We examine a prevalent model in aeroelasticity which describes the transverse oscillations of a plate immersed in a laminar flow. The model comprises a perturbed wave equation strongly coupled to a nonlinear plate; including nonlinearity in the model is essential for accuracy. For the last 50 years, this flow-plate system has been studied primarily from the numerical point of view. In particular, the key focus in aeroelasticity is the prediction and suppression of an endemic instability termed flutter, wherein the structure's natural vibrational modes couple with the aerodynamic load.
Recent advances over the last 15 years in the theory of nonlinear plates have allowed us to consider the system from the infinite dimensional point of view, making the flow-plate system amenable to semigroup, control theoretic, and long-time behavior analyses. In this talk we discuss the key physical parameters in the analysis: the plate thickness and the unperturbed flow velocity. Both of these parameters are critical in determining the properties of the dynamics. We will (1) present key (semigroup) well-posedness results and (2) discuss the addition of mechanical or frictional damping to the system in order to obtain the existence of global attractors (ultimate compactness and finite dimensionality of trajectories).