Monica Musso (University of Bath)
Title: Long time behavior for vortex dynamics in the 2 dimensional Euler
equations
Abstract: The evolution of a two dimensional incompressible ideal fluid with smooth initial
vorticity concentrated in small regions is well understood on finite intervals of time: it
converges to a super position of Dirac deltas centered at collision-less solutions to the
point vortex system, in the limit of vanishing regions. Even though for generic initial
conditions the vortex point system has a global smooth solution, much less is known on the
long time behavior of the fluid vorticity.
We consider the case of two vortex pairs traveling in opposite directions. Using gluing
methods we describe the global dynamics of this configuration. This work is in
collaboration with J Davila (U. of Bath), M. del Pino (U of Bath) and S. Parmeshwar
(Warwick University).