{
  "id": "1704.07354",
  "version": "v1",
  "published": "2017-04-24T17:48:21.000Z",
  "updated": "2017-04-24T17:48:21.000Z",
  "title": "Global weak solution to the viscous two-phase model with finite energy",
  "authors": [
    "Alexis Vasseur",
    "Huanyao Wen",
    "Cheng Yu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove the existence of global weak solutions to the compressible Navier-Stokes equations when the pressure law is in two variables.The method is based on the Lions argument and the Feireisl-Novotny-Petzeltova method. The main contribution of this paper is to develop a new argument for handling a nonlinear pressure law $P(\\rho,n)=\\rho^{\\gamma}+n^{\\alpha}$ where $\\rho,\\,n$ satisfy the mass equations. This yields the strong convergence of the densities, and provides the existence of global solutions in time, for the compressible barotropic Navier-Stokes equations, with large data. The result holds in three space dimensions on condition that the adiabatic constants $\\gamma>\\frac{9}{5}$ and $\\alpha\\geq 1$. Our result is the first global existence theorem on the viscous compressible two-phase model with pressure law in two variables, for large initial data, in the multidimensional space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-24T17:48:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global weak solution",
      "viscous two-phase model",
      "finite energy",
      "first global existence theorem",
      "barotropic navier-stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}