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The elimination of aeroelastic instability (resulting in sustainedoscillations of bridges, buildings, airfoils) is a central engineering anddesign issue. Mathematically, this translates to strong asymptoticstabilization of a 3D flow by a 2D elastic structure. The stabilization(convergence to the stationary set) of a aerodynamic wave-plate model isestablished here. A 3D potential flow on the half-space has a spatially-boundedvon Karman plate embedded in the boundary. The physical model, then, is aNeumann wave equation with low regularity of coupling conditions. Motivated onempirical observations, we examine if intrinsic panel damping can stabilize thesubsonic flow-plate system to a stationary point. Several partial results havebeen established through partial regularization of the model. Without doing so,classical approaches attempting to treat the given wave boundary data havefallen short, owing to the failure of the Lopatinski condition (in the sense ofKreiss, Sakamoto) and the associated regularity defect of the hyperbolicNeumann mapping. Here, we operate on the panel model as in the engineeringliterature with no regularization or modifications; we completely resolve thequestion of stability by demonstrating that weak plate damping stronglystabilizes system trajectories. This is accomplished by microlocalizing thewave data (given by the plate) and observing an "anisotropic" a microlocalcompensation by the plate dynamics precisely where the regularity of the 3Dwave is compromsed (in the characteristic sector). Several additional stabilityresults for both wave and plate subsystems are established to "push" strongstability of the plate onto the flow.

Strong Stabilization of a 3D Potential Flow via a Weakly Damped von Karman Plate