{
  "id": "1803.00066",
  "version": "v1",
  "published": "2018-02-28T20:21:17.000Z",
  "updated": "2018-02-28T20:21:17.000Z",
  "title": "Gluing methods for vortex dynamics in Euler flows",
  "authors": [
    "Juan Davila",
    "Manuel del Pino",
    "Monica Musso",
    "Juncheng Wei"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "A classical problem for the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. is that of finding regular solutions with highly concentrated vorticities around $N$ moving {\\em vortices}. The formal dynamic law for such objects was first derived in the 19th century by Kirkhoff and Routh. In this paper we devise a {\\em gluing approach} for the construction of smooth $N$-vortex solutions. We capture in high precision the core of each vortex as a scaled finite mass solution of Liouville's equation plus small, more regular terms. Gluing methods have been a powerful tool in geometric constructions by {\\em desingularization}. We succeed in applying those ideas in this highly challenging setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-28T20:21:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gluing methods",
      "vortex dynamics",
      "liouvilles equation plus small",
      "formal dynamic law",
      "scaled finite mass solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}