{
  "id": "1212.2867",
  "version": "v2",
  "published": "2012-12-12T16:29:28.000Z",
  "updated": "2013-05-06T03:28:19.000Z",
  "title": "Compressible Flow and Euler's Equations",
  "authors": [
    "Demetrios Christodoulou",
    "Shuang Miao"
  ],
  "comment": "505 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "physics.flu-dyn"
  ],
  "abstract": "We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the inverse density of the wave fronts vanishes and the shocks form. We obtain a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-06T03:28:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compressible flow",
      "constant state outside",
      "initial data corresponds",
      "maximal solution contains",
      "wave fronts vanishes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 505,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.2867C"
    }
  }
}