{
  "id": "1902.08642",
  "version": "v1",
  "published": "2019-02-22T19:22:15.000Z",
  "updated": "2019-02-22T19:22:15.000Z",
  "title": "The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface",
  "authors": [
    "Fernando A Morales"
  ],
  "comment": "27 pages, 4 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "The asymptotic analysis of a Darcy-Stokes system modeling the fluid exchange between a narrow channel (Stokes) and a porous medium (Darcy) coupled through a $ C^{2} $ curved interface, is presented. The channel is a cylindrical domain between the interface ($ \\Gamma $) and a parallel translation of it ($ \\Gamma + \\epsilon \\, \\boldsymbol{\\widehat{e}}_{N} $). The introduction of a change variable to fix the domain's geometry and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find a Darcy-Brinkman lower dimensional coupled system as the limiting form, when the width of the channel tends to zero ($ \\epsilon \\rightarrow 0 $).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-22T19:22:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "80M40",
      "76S99",
      "58J05",
      "76M45"
    ],
    "keywords": [
      "asymptotic analysis",
      "darcy-stokes system",
      "curved interface",
      "darcy-brinkman lower dimensional coupled system",
      "introduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}