Asymptotic Stabilizability by Stationary Feedback of the Two-Dimensional Euler Equation: The Multiconnected Case

We construct a feedback law which allows us to asymptotically stabilize the Euler system for incompressible inviscid fluids in two dimensions, in the case of a multiconnected bounded domain, by means of a control localized on a part of the boundary that meets every connected component of the boundary. This generalizes a result of Coron [{SIAM J. Control Optim., 37 (1999), pp. 1874-1896] concerning simply connected domains.