{
  "id": "1905.01970",
  "version": "v1",
  "published": "2019-04-21T12:49:48.000Z",
  "updated": "2019-04-21T12:49:48.000Z",
  "title": "The pressureless limits of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow with a source term",
  "authors": [
    "Shouqiong Sheng",
    "Zhiqiang Shao"
  ],
  "comment": "18 pages. arXiv admin note: substantial text overlap with arXiv:1904.05176, arXiv:1904.03462",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the limits of Riemann solutions to the inhomogeneous Euler equations of one-dimensional compressible fluid flow as the adiabatic exponent $\\gamma$ tends to one. Different from the homogeneous equations, the Riemann solutions of the inhomogeneous system are non self-similar. It is rigorously shown that, as $\\gamma$ tends to one, any two-shock Riemann solution tends to a delta shock solution of the pressureless Euler system with a source term, and the intermediate density between the two shocks tends to a weighted $\\delta$-mesaure which forms the delta shock; while any two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution of the pressureless Euler system with a source term, whose intermediate state between the two contact discontinuities is a vacuum state. Moreover, we also give some numerical results to confirm the theoretical analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-21T12:49:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional compressible fluid flow",
      "source term",
      "euler equations",
      "pressureless limits",
      "pressureless euler system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}