{
  "id": "1904.00437",
  "version": "v1",
  "published": "2019-03-31T15:45:09.000Z",
  "updated": "2019-03-31T15:45:09.000Z",
  "title": "Uniqueness result for the 3-D Navier-Stokes-Boussinesq equations with horizontal dissipation",
  "authors": [
    "Haroune Houamed",
    "Pierre Dreyfuss"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, for the 3-D Navier-Stokes-Boussinesq system with horizontal dissipation, where there is no smoothing effect on the vertical derivatives, we prove a uniqueness result of solutions $ (u,\\rho)\\in L^{\\infty}_T\\big( H^{0,s}\\times H^{0,1-s}\\big)$ with $ (\\nabla_h u,\\nabla_h\\rho)\\in L^{2}_T\\big( H^{0,s}\\times H^{0,1-s}\\big)$ and $s\\in [1/2,1]$. As a consequence, we improve the conditions stated in the paper \\cite{Miao} in order to obtain a global well-posedness result in the case of axisymmetric initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-31T15:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "76D05",
      "35B33",
      "35Q35"
    ],
    "keywords": [
      "horizontal dissipation",
      "uniqueness result",
      "navier-stokes-boussinesq equations",
      "global well-posedness result",
      "axisymmetric initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}