{
  "id": "1808.09605",
  "version": "v1",
  "published": "2018-08-29T02:11:27.000Z",
  "updated": "2018-08-29T02:11:27.000Z",
  "title": "Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations for Compressible Fluid Flow with vacuum",
  "authors": [
    "Yongcai Geng",
    "Yachun Li",
    "Shengguo Zhu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible Navier-Stokes equations with density-dependent viscosities, arbitrarily large initial data and vacuum, whose life span is uniformly positive in the vanishing viscosity limit. It is worth paying special attention that, via introducing a \"quasi-symmetric hyperbolic\"--\"degenerate elliptic\" coupled structure, we can also give some uniformly bounded estimates of $\\displaystyle\\Big(\\rho^{\\frac{\\gamma-1}{2}}, u\\Big)$ in $H^3$ space and $\\rho^{\\frac{\\delta-1}{2}}$ in $H^2$ space (adiabatic exponent $\\gamma>1$ and $1<\\delta \\leq \\min\\{3, \\gamma\\}$), which lead the strong convergence of the regular solution of the viscous flow to that of the inviscid flow in $L^{\\infty}([0, T]; H^{s'})$ (for any $s'\\in [2, 3)$) space with the rate of $\\epsilon^{2(1-s'/3)}$. Further more, we point out that our framework in this paper is applicable to other physical dimensions, say 1 and 2, with some minor modifications. This paper is based on our early preprint in 2015.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T02:11:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vanishing viscosity limit",
      "navier-stokes equations",
      "compressible fluid flow",
      "euler equations",
      "unique regular solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}