{
  "id": "1103.3763",
  "version": "v1",
  "published": "2011-03-19T07:41:09.000Z",
  "updated": "2011-03-19T07:41:09.000Z",
  "title": "Holder continuity for a drift-diffusion equation with pressure",
  "authors": [
    "Luis Silvestre",
    "Vlad Vicol"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We address the persistence of H\\\"older continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressure \\[ u_t + b \\cdot \\grad u - \\lap u = \\grad p,\\qquad \\grad\\cdot u =0 \\] on $[0,\\infty) \\times \\R^{n}$, with $n \\geq 2$. The drift velocity $b$ is assumed to be at the critical regularity level, with respect to the natural scaling of the equations. The proof draws on Campanato's characterization of H\\\"older spaces, and uses a maximum-principle-type argument by which we control the growth in time of certain local averages of $u$. We provide an estimate that does not depend on any local smallness condition on the vector field $b$, but only on scale invariant quantities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-19T07:41:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35B65",
      "35R05"
    ],
    "keywords": [
      "holder continuity",
      "linear drift-diffusion equation",
      "local smallness condition",
      "scale invariant quantities",
      "drift velocity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012AnIHP..29..637S"
    }
  }
}