{
  "id": "math/0702170",
  "version": "v1",
  "published": "2007-02-07T08:45:12.000Z",
  "updated": "2007-02-07T08:45:12.000Z",
  "title": "Existence and uniqueness results for viscous, heat-conducting 3-D fluid with vacuum",
  "authors": [
    "Ting Zhang",
    "Daoyuan Fang"
  ],
  "comment": "36 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. We prove the local existence and uniqueness of the strong solution in a domain $\\Omega\\subset\\mathbb{R}^3$. The initial density may vanish in an open set and $\\Omega$ could be a bounded or unbounded domain. We also prove a blow-up criterion for the solution. Finally, we show the blow-up of the smooth solution to the compressible Navier-Stokes equations in $\\mathbb{R}^n$ ($n\\geq1$) when the initial density has compactly support and the initial total momentum is nonzero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-07T08:45:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76N10"
    ],
    "keywords": [
      "uniqueness results",
      "thermal conductivity coefficient depend",
      "initial density",
      "full navier-stokes equations",
      "initial total momentum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2170Z"
    }
  }
}