{
  "id": "1501.06291",
  "version": "v1",
  "published": "2015-01-26T09:13:29.000Z",
  "updated": "2015-01-26T09:13:29.000Z",
  "title": "On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity",
  "authors": [
    "Xiangdi Huang",
    "Zhouping Xin"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "It is known that smooth solutions to the non-isentropic Navier-Stokes equations without heat-conductivity may lose their regularities in finite time in the presence of vacuum. However, in spite of the recent progress on such blowup phenomenon, it remain to give a possible blowup mechanism. In this paper, we present a simple continuation principle for such system, which asserts that the concentration of the density or the temperature occurs in finite time for a large class of smooth initial data, which is responsible for the breakdown of classical solutions. It also give an affirmative answer to a strong version of conjecture proposed by J.Nash in 1950s",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-26T09:13:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35B65",
      "76N10"
    ],
    "keywords": [
      "non-isentropic navier-stokes equations",
      "heat-conductivity",
      "finite time",
      "singularity",
      "smooth initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150106291H"
    }
  }
}