Seminar in Analysis: Evelyne Miot
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.