{
  "id": "2209.06075",
  "version": "v1",
  "published": "2022-09-13T15:30:27.000Z",
  "updated": "2022-09-13T15:30:27.000Z",
  "title": "Homogenization of the Navier-Stokes equations in perforated domains in the inviscid limit",
  "authors": [
    "Richard M. Höfer"
  ],
  "comment": "All comments welcome!",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the solution $u_\\varepsilon$ to the Navier-Stokes equations in $\\mathbb R^3$ perforated by small particles centered at $(\\varepsilon \\mathbb Z)^3$ with no-slip boundary conditions at the particles. We study the behavior of $u_\\varepsilon$ for small $\\varepsilon$, depending on the diameter $\\varepsilon^\\alpha$, $\\alpha > 1$, of the particles and the viscosity $\\varepsilon^\\gamma$, $\\gamma > 0$, of the fluid. We prove quantitative convergence results for $u_\\varepsilon$ in all regimes when the local Reynolds number at the particles is negligible. Then, the particles approximately exert a linear friction force on the fluid. The obtained effective macroscopic equations depend on the order of magnitude of the collective friction. We obtain a) the Euler-Brinkman equations in the critical regime, b) the Euler equations in the subcritical regime and c) Darcy's law in the supercritical regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-13T15:30:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35Q31",
      "76D07",
      "76M50",
      "76S05",
      "76T25"
    ],
    "keywords": [
      "navier-stokes equations",
      "inviscid limit",
      "perforated domains",
      "homogenization",
      "local reynolds number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}