{
  "id": "1208.1199",
  "version": "v2",
  "published": "2012-08-06T16:12:19.000Z",
  "updated": "2017-02-21T14:02:04.000Z",
  "title": "Global solutions to the three-dimensional full compressible Navier-Stokes equations with vacuum at infinity in some classes of large data",
  "authors": [
    "Huanyao Wen",
    "Changjiang Zhu"
  ],
  "comment": "57 pages",
  "journal": "SIAM J. Math. Anal. 49, no. 1, 162-221 (2017)",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the large-time behavior of the solutions as well as the decay rates in time. Our main results show that the strong solution exists globally in time if the initial mass is small for the fixed coefficients of viscosity and heat conduction, and can be large for the large coefficients of viscosity and heat conduction. Moreover, large-time behavior and a surprisingly exponential decay rate of the strong solution are obtained. Finally, we show that the global strong solution can become classical if the initial data is more regular. Note that the assumptions on the initial density do not exclude that the initial density may vanish in a subset of R3 and that it can be of a non trivially compact support.To our knowledge, this paper contains the first result so far for the global existence of solutions to the full compressible Navier-Stokes equations when density vanishes at infinity (in space). In addition, the exponential decay rate of the strong solution is of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-06T16:12:19.000Z",
      "title": "Global classical solution to 3D full compressible Navier-Stokes equations with vacuum at infinity",
      "abstract": "In this paper, we prove that there exists a unique global strong solution to the three-dimensional full compressible Navier-Stokes equations with vacuum at infinity, provided that the initial mass is small in some sense. The initial vacuum may also appear in a subset of $R^3$ besides at infinity, or can be of compact support. Our result shows that the initial mass can be large if the coefficients of viscosity and heat conduction are taken to be large, which implies that large viscosity and heat conduction mean large solution. Furthermore, large time behavior and decay estimates of the strong solution are considered, and some necessary conditions also are given for global strong solution with momentum or energy conservation. Finally, we show that the global strong solution can become classical if the initial data is more regular.",
      "comment": "45 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-02-21T14:02:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d full compressible navier-stokes equations",
      "global classical solution",
      "global strong solution",
      "conduction mean large solution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1199W"
    }
  }
}