53rd Midwest PDE Seminar March 19-21, 2004 Department of Mathematics University of Missouri

Gustavo Ponce University of California Santa Barbara
On the interaction of nearly parallel vortex filaments (joint work with C.E. Kenig and L.Vega)

Abstract

The system for the interaction of nearly parallel vortex filaments deduced by Klein, Majda and Damodaran is considered. Local existence for the associated initial value problem with data which are small perturbations of perfect parallel filaments is proved. Assumptions on the unperturbed configurations and on the initial parameters which guarantee the existence of global regular solutions (no finite time collapse) are deduced.