{
  "id": "1208.6374",
  "version": "v1",
  "published": "2012-08-31T06:05:58.000Z",
  "updated": "2012-08-31T06:05:58.000Z",
  "title": "Lagrangian flows for vector fields with gradient given by a singular integral",
  "authors": [
    "François Bouchut",
    "Gianluca Crippa"
  ],
  "journal": "Journal of Hyperbolic Differential Equations 10, 2 (2013) 235-282",
  "doi": "10.1142/S0219891613500100",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an $L^1$ function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the $BV$ theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-31T06:05:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector field",
      "singular integral",
      "lagrangian flows",
      "ordinary differential equations",
      "transport equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.6374B"
    }
  }
}