Nonlinear plates interacting with a subsonic, inviscid flow via Kutta-Joukowski interface conditions

We present results on well-posedness of the fluid-structure interaction with the Kutta-Joukowski flow conditions in force. The semigroup approach to the proof utilizes an abstract setup related to that in Chueshov et al. (2013) but requires (1) the use of a Neumann-flow map to address a Zaremba type elliptic problem and (2) a trace regularity assumption on the acceleration potential of the flow. This assumption is linked to invertibility of singular integral operators which are analogous to the finite Hilbert transform in two dimensions. (We show the validity of this assumption when the model is reduced to a two dimensional flow interacting with a one dimensional structure; this requires microlocal techniques.) Our results link the analysis in Chueshov (2013) to that in Balakrishnan (2012, 2007).