{
  "id": "1603.07479",
  "version": "v1",
  "published": "2016-03-24T08:51:46.000Z",
  "updated": "2016-03-24T08:51:46.000Z",
  "title": "Global persistence of geometrical structures for the boussinesq equation with no diffusion",
  "authors": [
    "Raphaël Danchin",
    "Xin Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Here we investigate the so-called temperature patch problem for the incompressible Boussinesq system with partial viscosity, in the whole space $\\mathbb{R}^N$ $(N \\geq 2)$, where the initial temperature is the characteristic function of some simply connected domain with $C^{1, \\varepsilon}$ H{\\\"o}lder regularity. Although recent results in [1, 15] ensure that an initially $C^1$ patch persists through the evolution, whether higher regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue globally in time, in the 2-D case for large initial data and in the higher dimension case for small initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-24T08:51:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boussinesq equation",
      "global persistence",
      "geometrical structures",
      "small initial data",
      "large initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307479D"
    }
  }
}