| Abstract: |
| In this talk, we will discuss vortex motions for Euler equations in planar domains. In this setting, the dynamics of a single vortex is governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that, under certain non-degeneracy conditions, it is possible to desingularize most of these trajectories into time-periodic concentrated vortex patches. The proof uses a Nash-Moser scheme and KAM techniques combined with complex geometry tools. Additionally, we will present a vortex duplication mechanism to generate synchronized time-periodic motion of multiple vortices. This is a joint work with Taoufik Hmidi and Emeric Roulley.setting, the dynamics of a single vortex is governed by a Hamiltonian system, with most
of its energy levels corresponding to time-periodic motion. We show that, under certain |
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