{
  "id": "1104.2516",
  "version": "v1",
  "published": "2011-04-13T14:46:08.000Z",
  "updated": "2011-04-13T14:46:08.000Z",
  "title": "Decay Estimates for Isentropic Compressible Navier-Stokes Equations in Bounded Domain",
  "authors": [
    "Daoyuan Fang",
    "Ruizhao Zi",
    "Ting Zhang"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, under the hypothesis that $\\rho$ is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible Navier-Stokes equations and show that the weak solutions decay exponentially to the equilibrium state in $L^2$ norm. This can be regarded as a generalization of Matsumura and Nishida's results in 1982, since our analysis is done in the framework of Lions 1998 and Feireisl et al. 2001, the higher regularity of $(\\rho, u)$ and the uniformly positive lower bound of $\\rho$ are not necessary in our analysis and vacuum may be admitted. Indeed, the upper bound of the density $\\rho$ plays the essential role in our proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-13T14:46:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decay estimates",
      "bounded domain",
      "upper bound",
      "multidimensional isentropic compressible navier-stokes equations",
      "weak solutions decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.2516F"
    }
  }
}