| Abstract: |
| The evolution of a two-dimensional incompressible ideal fluid with smooth initial vorticity concentrated in small regions is well understood over finite time intervals: as these regions shrink to zero, the vorticity converges to a superposition of Dirac deltas centered on collision-free solutions of the point vortex system. Although the point vortex system exhibits globally smooth solutions for generic initial conditions, the long-term behavior of the fluid vorticity remains much less understood.
We consider two scenarios: the case of two vortex pairs traveling in opposite directions and that of an expanding self-similar configuration of vortices. Using gluing methods we describe the global dynamics of this configuration. This work is in collaboration with J Davila, M. del Pino and S. Parmeshwar. |
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