Incompressible flow around thin obstacle, uniqueness for the wortex-wave system

Abstract

We present here the results concerning the inuence of a thin obstacle on the behavior of incompressible ow. We extend the works made by Itimie, Lopes Filho, Nussenzveig Lopes and Kelliher where they consider that the obstacle shrinks to a point. We begin by working in two-dimension, and thanks to complex analysis we treat the case of ideal and viscous ows around a curve. Next, we consider three-dimensional viscous ow in the exterior of a surface/curve. We nish by giving uniqueness of the vortex- wave system with a single point vortex introduced by Marchioro and Pulvirenti, in the case where the initial vorticity is constant near the point vortex. This last result gives, in particular, the uniqueness of the limit system obtained in the case of a perfect uid around a point. We choose here to give the main steps of this uniqueness result, obtained in collaboration with E. Miot.