{
  "id": "0706.1969",
  "version": "v1",
  "published": "2007-06-13T18:55:36.000Z",
  "updated": "2007-06-13T18:55:36.000Z",
  "title": "Formation of singularities for a transport equation with nonlocal velocity",
  "authors": [
    "Antonio Cordoba",
    "Diego Cordoba",
    "Marco A. Fontelos"
  ],
  "comment": "13 pages, published version",
  "journal": "Ann. of Math. (2) 162 (2005), no. 3, 1377--1389",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-13T18:55:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlocal velocity",
      "1d transport equation",
      "finite time singularity",
      "initial data",
      "diffusion term"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1969C"
    }
  }
}