| Abstract: |
| We consider the Euler equations within a simply-connected bounded domain. The dynamics of a single point vortex are governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that for the single point vortex, under certain non-degeneracy conditions, it is possible to desingularize most of these trajectories into time-periodic concentrated vortex patches. We provide concrete examples of domains where these non-degeneracies are satisfied, in particular convex ones. We also present a duplication method to construct synchronized motion of several vortices. |
|