Seminar Analysis: Evelyne Miot (CNRS & Paris Orsay)

Global existence and collisions for some configurations of nearly parallel vortex filaments

A system of simplified equations has been derived by Klein, Majda and Damodaran to describe the dynamics of nearly parallel vortex filaments in incompressible 3D fluids. This system combines a 1D Schrödinger-type structure together with the 2D point vortex system. Global existence for small perturbations of exact parallel filaments has been established by Kenig, Ponce and Vega in the case of two filaments and for particular configurations of three filaments. In this talk I will present large time existence results for particular configurations of four filaments and for other particular configurations of N filaments for any N larger than 2. I will also discuss some situations of finite time filament collapse. This is joint work with Valeria Banica.

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