{
  "id": "1912.07901",
  "version": "v1",
  "published": "2019-12-17T09:48:00.000Z",
  "updated": "2019-12-17T09:48:00.000Z",
  "title": "Derivation of an intermediate viscous Serre--Green--Naghdi equation",
  "authors": [
    "Denys Dutykh",
    "Hervé Le Meur"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this note we present the current status of the derivation of a viscous Serre-Green-Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier-Stokes equations. We consider a particular regime linking the Reynolds number and the shallowness parameter. The computations presented in this note are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prantdl-like equation. Further approximations seem to be needed to obtain a tractable model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T09:48:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intermediate viscous serre-green-naghdi equation",
      "derivation",
      "boundary layer flow reduces",
      "inviscid euler equations",
      "current status"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}