{
  "id": "0909.2557",
  "version": "v1",
  "published": "2009-09-14T14:31:52.000Z",
  "updated": "2009-09-14T14:31:52.000Z",
  "title": "Uniqueness and Instability of Subsonic--Sonic Potential Flow in A Convergent Approximate Nozzle",
  "authors": [
    "Pan Liu",
    "Hairong Yuan"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We proved uniqueness and instability of the symmetric subsonic--sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross--sections. Such a surface may be regarded as an approximation of a two--dimensional convergent nozzle in aerodynamics. Mathematically these are uniqueness and nonexistence results of a nonlinear degenerate elliptic equation with Bernoulli type boundary conditions. The proof depends on maximum principles and a generalized Hopf boundary point lemma which was proved in the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-14T14:31:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "35B50",
      "76H05"
    ],
    "keywords": [
      "convergent approximate nozzle",
      "subsonic-sonic potential flow",
      "uniqueness",
      "instability",
      "symmetric subsonic-sonic flow solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2557L"
    }
  }
}