2015/07/02 by Valeria Banica, Erwan Faou, Banica, Valeria +4
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Quantum, superfluid, helium dynamics #math.AP
paper · pdf · doi:10.48550/arxiv.1507.00549
arxiv created 2015/07/02 · openalex publication_date 2015/07/02 · arxiv updated 2015/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda and Damodaran [KMD95] and Zakharov [Z88,Z99]. 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 [BFM14]. In the second part of this paper we extend this construction to the case of an arbitrary number of filaments, with polygonial symmetry, that are perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity.