{
  "id": "1502.05579",
  "version": "v1",
  "published": "2015-02-19T14:19:06.000Z",
  "updated": "2015-02-19T14:19:06.000Z",
  "title": "Equilibria of point-vortices on closed surfaces",
  "authors": [
    "Teresa D'Aprile",
    "Pierpaolo Esposito"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface $\\Sigma$. The topological properties of $\\Sigma$ determine the occurrence of three distinct situations, corresponding to $\\mathbb{S}^2$, to $\\mathbb{RP}^2$ and to $\\Sigma \\not=\\mathbb{S}^2,\\mathbb{RP}^2$. As a by-product, we also obtain new existence results for the singular mean-field equation with exponential nonlinearity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-19T14:19:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35J61",
      "35J20",
      "76B47"
    ],
    "keywords": [
      "closed surface",
      "point-vortices",
      "hamiltonian point-vortex model",
      "singular mean-field equation",
      "distinct situations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}