Valeria BANICA - Collision of almost parallel vortex filaments
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2016-07-04

We investigate the occurrence of collisions in the evolution of vortex filaments through a system  introduced  by  Klein,  Majda  and  Damodaran  and by  Zakharov.  We  first  establish  rigorously  the existence  of  a  pair  of almost  parallel  vortex  filaments,  with  opposite circulation, colliding at some point in finite time. The collision mechanism is based on the one  of  the  self-similar  solutions  of  the  model,  described  in  our previous  work.  We also extend  this  construction  to  the  case  of  an
arbitrary  number  of  filaments,  with  polygonal symmetry, that are
perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity. 
This is a joint work with Erwan Faou and Evelyne Miot.