{
  "id": "math/0703621",
  "version": "v1",
  "published": "2007-03-21T05:20:45.000Z",
  "updated": "2007-03-21T05:20:45.000Z",
  "title": "Existence and asymptotic behavior of $C^1$ solutions to the multidimensional compressible Euler equations with damping",
  "authors": [
    "Daoyuan Fang",
    "Jiang Xu"
  ],
  "comment": "18 pages",
  "journal": "Nonlinear Anal. TMA 70(2009) 244-261",
  "doi": "10.1016/j.na.2007.11.049",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, the existence and asymptotic behavior of $C^1$ solutions to the multidimensional compressible Euler equations with damping on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve the well-posedness results of Sideris-Thomases-Wang (Comm.P.D.E. 28 (2003) 953). The global existence lies on a crucial a-priori estimate which is proved by the spectral localization method. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-21T05:20:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "76N15"
    ],
    "keywords": [
      "multidimensional compressible euler equations",
      "asymptotic behavior",
      "global existence lies",
      "crucial a-priori estimate",
      "spectral localization method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3621F"
    }
  }
}