{
  "id": "1807.00550",
  "version": "v1",
  "published": "2018-07-02T09:14:46.000Z",
  "updated": "2018-07-02T09:14:46.000Z",
  "title": "Global Existence of the Compressible Euler Equations with Time-dependent Damping and Sign-changing State Equation",
  "authors": [
    "Ka Luen Cheung",
    "Sen Wong"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In mathematical physics, the pressure function is determined by the equation of state. There are two existing state equations: the state equation (S+) for polytropic gas with adiabatic index greater than 1 and the state equation (S-) for generalized Chaplygin gas in cosmology. In this paper, we provide some mathematical foundations for the sign-changing pressure (S*) by establishing a global existence result for the one-dimensional Euler equations with time-dependent damping. It is found that the newly introduced sign-changing pressure shares many mathematical properties such as reduction to a symmetric hyperbolic system and finite propagation speed property with the classical positive pressure S+ and the negative pressure S-. Moreover, S+ and S- are unified and generalized in our proposition which includes a global existence result for S+, S- and S*.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T09:14:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compressible euler equations",
      "sign-changing state equation",
      "time-dependent damping",
      "global existence result",
      "one-dimensional euler equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}