{
  "id": "0910.0596",
  "version": "v6",
  "published": "2009-10-04T11:47:55.000Z",
  "updated": "2010-06-04T06:18:10.000Z",
  "title": "The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces",
  "authors": [
    "Ryôhei Kakizawa"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the abstract initial value problem for the system of evolution equations which describe motion of incompressible viscous and heat-conductive fluids in a bounded domain. It is difficulty of our problem that we do not neglect the viscous dissipation function in contrast to the Boussinesq approximation. This problem has uniquely a mild solution locally in time for general initial data, and globally in time for small initial data. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banach spaces.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2010-06-04T06:18:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K90",
      "35Q35",
      "76D03"
    ],
    "keywords": [
      "banach spaces",
      "heat-conductive fluids",
      "incompressible viscous",
      "mild solution",
      "abstract initial value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0596K"
    }
  }
}