Uniqueness for the vortex-wave system when the vorticity is constant   near the point vortex
  We prove uniqueness for the vortex-wave system with a single point vortex introduced by Marchioro and Pulvirenti in the case where the vorticity is initially constant near the point vortex. Our method relies on the Eulerian approach for this problem and in particular on the formulation in terms of the velocity. 
Christophe Lacave (ICJ), Evelyne Miot (LJLL)