{
  "id": "1507.00549",
  "version": "v1",
  "published": "2015-07-02T12:39:11.000Z",
  "updated": "2015-07-02T12:39:11.000Z",
  "title": "Collision of almost parallel vortex filaments",
  "authors": [
    "Valeria Banica",
    "Erwan Faou",
    "Evelyne Miot"
  ],
  "categories": [
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-02T12:39:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant angular velocity",
      "arbitrary number",
      "opposite circulation",
      "self-similar solutions",
      "second part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}