{
  "id": "2202.13385",
  "version": "v1",
  "published": "2022-02-27T15:32:05.000Z",
  "updated": "2022-02-27T15:32:05.000Z",
  "title": "The time asymptotic expansion for the compressible Euler equations with time-dependent damping",
  "authors": [
    "Shifeng Geng",
    "Feimin Huang",
    "Guanghui Jin",
    "Xiaochun Wu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the compressible Euler equations with time-dependent damping $-\\frac{1}{(1+t)^{\\lambda}}\\rho u$. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME) and rigorously justify this expansion as $\\lambda \\in (\\frac17,1)$. In other word, instead of the self-similar solution of GPME, the expansion is the best asymptotic profile of the solution to the compressible Euler equations with time-dependent damping.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-27T15:32:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compressible euler equations",
      "time asymptotic expansion",
      "time-dependent damping",
      "self-similar solution",
      "generalized porous media equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}