{
  "id": "1510.03237",
  "version": "v1",
  "published": "2015-10-12T11:48:48.000Z",
  "updated": "2015-10-12T11:48:48.000Z",
  "title": "Global smooth solution to the 2D Boussinesq equations with fractional dissipation",
  "authors": [
    "Zhuan Ye"
  ],
  "comment": "19 pages. arXiv admin note: text overlap with arXiv:1506.08993",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the two-dimensional (2D) incompressible Boussinesq system with fractional Laplacian dissipation and thermal diffusion. Based on the previous works and some new observations, we show that the condition $1-\\alpha <\\beta<\\min\\Big\\{\\frac{\\alpha}{2},\\,\\,\\frac{3\\alpha-2}{2(2-\\alpha)(1-\\alpha)},\\,\\, \\frac{3\\alpha^{2}+4\\alpha-4}{8(1-\\alpha)}\\Big\\}$ with $0.7351\\approx\\frac{10-2\\sqrt{10}}{5}<\\alpha\\leq \\frac{4}{5}$ suffices in order for the solution pair of velocity and temperature to remain smooth for all time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-12T11:48:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35B65",
      "76D03"
    ],
    "keywords": [
      "2d boussinesq equations",
      "global smooth solution",
      "fractional dissipation",
      "fractional laplacian dissipation",
      "incompressible boussinesq system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151003237Y"
    }
  }
}