{
  "id": "1506.00470",
  "version": "v1",
  "published": "2015-06-01T12:26:04.000Z",
  "updated": "2015-06-01T12:26:04.000Z",
  "title": "Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation",
  "authors": [
    "Zhuan Ye",
    "Xiaojing Xu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Abstract: As a continuation of the previous work [40], in this paper we focus on the Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation. We give an elementary proof of the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. The argument is based on the nonlinear lower bounds for the fractional Laplacian established in [12]. Consequently, this result significantly improves the recent works [12, 38, 40].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-01T12:26:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35B65",
      "76D03"
    ],
    "keywords": [
      "fractional laplacian dissipation",
      "2d boussinesq equations",
      "global well-posedness",
      "nonlinear lower bounds",
      "global regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}