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Mathematics > Analysis of PDEs

arXiv:1507.00549 (math)
[Submitted on 2 Jul 2015]

Title:Collision of almost parallel vortex filaments

Authors:Valeria Banica, Erwan Faou, Evelyne Miot
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Abstract: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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1507.00549 [math.AP]
  (or arXiv:1507.00549v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1507.00549

Submission history

From: Valeria Banica [view email]
[v1] Thu, 2 Jul 2015 12:39:11 UTC (19 KB)
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