{
  "id": "2402.02531",
  "version": "v1",
  "published": "2024-02-04T15:25:53.000Z",
  "updated": "2024-02-04T15:25:53.000Z",
  "title": "Non-existence of classical solutions to a two-phase flow model with vacuum",
  "authors": [
    "Hai-Liang Li",
    "Yuexun Wang",
    "Yue Zhang"
  ],
  "doi": "10.1088/1361-6544/add231",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the well-posedness of classical solutions to a two-phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier-Stokes equations via a drag forcing term. We consider the case that the fluid densities may contain a vacuum, and the viscosities are density-dependent functions. Under suitable assumptions on the initial data, we show that the finite-energy (i.e., in the inhomogeneous Sobolev space) classical solutions to the Cauchy problem of this coupled system do not exist for any small time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-04T15:25:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "76N06",
      "35Q31"
    ],
    "keywords": [
      "classical solutions",
      "non-existence",
      "isentropic compressible navier-stokes equations",
      "small time",
      "two-phase flow model consisting"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}