{
  "id": "1107.3371",
  "version": "v1",
  "published": "2011-07-18T07:44:49.000Z",
  "updated": "2011-07-18T07:44:49.000Z",
  "title": "Fractional Laplacian with singular drift",
  "authors": [
    "Tomasz Jakubowski"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "For $\\alpha \\in (1,2)$ we consider the equation $\\partial_t u = \\Delta^{\\alpha/2} u - r b \\cdot \\nabla u$, where $b$ is a divergence free singular vector field not necessarily belonging to the Kato class. We show that for sufficiently small $r>0$ the fundamental solution is globally in time comparable with the density of the isotropic stable process",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-18T07:44:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular drift",
      "fractional laplacian",
      "divergence free singular vector field",
      "isotropic stable process",
      "fundamental solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.3371J"
    }
  }
}