{
  "id": "1402.5779",
  "version": "v1",
  "published": "2014-02-24T10:36:33.000Z",
  "updated": "2014-02-24T10:36:33.000Z",
  "title": "Asymptotic profiles for the third grade fluids equations",
  "authors": [
    "Olivier Coulaud"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the long time behaviour of the solutions of the third grade fluids equations in dimension 2. Introducing scaled variables and performing several energy estimates in weighted Sobolev spaces, we describe the first order of an asymptotic expansion of these solutions. It shows in particular that, under smallness assumptions on the data, the solutions of the third grade fluids equations converge to self-similar solutions of the heat equations, which can be computed explicitly from the data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-24T10:36:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic profiles",
      "third grade fluids equations converge",
      "long time behaviour",
      "heat equations",
      "self-similar solutions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.ijnonlinmec.2014.03.013",
      "journal": "International Journal of Non Linear Mechanics",
      "year": 2014,
      "month": "Oct",
      "volume": 65,
      "pages": 69
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014IJNLM..65...69C"
    }
  }
}