{
  "id": "2409.08457",
  "version": "v1",
  "published": "2024-09-13T01:07:52.000Z",
  "updated": "2024-09-13T01:07:52.000Z",
  "title": "$\\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space",
  "authors": [
    "Sri Maryani",
    "Miho Murata"
  ],
  "comment": "36 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider a resolvent problem arising from the free boundary value problem for the compressible fluid model of Korteweg type, which is called as the Navier-Stokes-Korteweg system, with surface tension in the half-space. The Navier-Stokes-Korteweg system is known as a diffuse interface model for liquid-vapor two-phase flows. Our purpose is to show the $\\mathcal R$-boundedness for the solution operator families of the resolvent problem, which gives us the maximal regularity estimates in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis's operator valued Fourier multiplier theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-13T01:07:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "76N10"
    ],
    "keywords": [
      "compressible fluid model",
      "bounded operator families arising",
      "korteweg type",
      "surface tension",
      "valued fourier multiplier theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}