{
  "id": "0910.4991",
  "version": "v2",
  "published": "2009-10-26T21:52:22.000Z",
  "updated": "2009-11-07T08:27:20.000Z",
  "title": "On a maximum principle and its application to logarithmically critical Boussinesq system",
  "authors": [
    "Taoufik Hmidi"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study a transport-diffusion model with some logarithmic dissipations. We look for two kinds of estimates. The first one is a maximum principle whose proof is based on Askey theorem concerning characteristic functions and some tools from the theory of $C_0$-semigroups. The second one is a smoothing effect based on some results from harmonic analysis and sub-Markovian operators. As an application we prove the global well-posedness for the two-dimensional Euler-Boussinesq system where the dissipation occurs only on the temperature equation and has the form $\\frac{\\DD}{\\log^\\alpha(e^4+\\DD)}$, with $\\alpha\\in[0,\\frac12]$. This result improves the critical dissipation $(\\alpha=0)$ needed for global well-posedness which was discussed in [15].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-11-07T08:27:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmically critical boussinesq system",
      "maximum principle",
      "application",
      "askey theorem concerning characteristic functions",
      "global well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.4991H"
    }
  }
}