{
  "id": "2009.03043",
  "version": "v1",
  "published": "2020-09-04T05:25:55.000Z",
  "updated": "2020-09-04T05:25:55.000Z",
  "title": "The global well-posedness of the compressible fluid model of Korteweg type for the critical case",
  "authors": [
    "Takayuki Kobayashi",
    "Miho Murata"
  ],
  "comment": "13 pages. arXiv admin note: substantial text overlap with arXiv:1908.07224",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the compressible fluid model of Korteweg type in a critical case where the derivative of pressure equals to $0$ at the given constant state. It is shown that the system admits a unique, global strong solution for small initial data in the maximal $L_p$-$L_q$ regularity class. As a result, we also prove the decay estimates of the solutions to the nonliner problem. In order to obtain the global well-posedness for the critical case, we show $L_p$-$L_q$ decay properties of solutions to the linearized equations under an additional assumption for a low frequencies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-04T05:25:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76N10"
    ],
    "keywords": [
      "compressible fluid model",
      "critical case",
      "korteweg type",
      "global well-posedness",
      "global strong solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}