{
  "id": "2407.11841",
  "version": "v1",
  "published": "2024-07-16T15:24:10.000Z",
  "updated": "2024-07-16T15:24:10.000Z",
  "title": "Asymptotic Analysis of Boundary Layers for Stokes Systems in Periodic Homogenization",
  "authors": [
    "Moustapha Agne"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the asymptotics of boundary layers in periodic homogenization. The analysis is focused on a Stokes system with periodic coefficients and periodic Dirichlet data posed in the half-space $\\{y\\in \\mathbb{R}^d: y\\cdot n -s>0\\}$. In particular, we establish the convergence of the velocity as $y\\cdot n \\rightarrow \\infty$. We obtain this convergence for arbitrary normals $n\\in \\mathbb{S}^{d-1}$. Moreover, we build an asymptotic expansion of Poisson's kernel for the periodically oscillating Stokes operator in the half-space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-16T15:24:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic homogenization",
      "boundary layers",
      "stokes system",
      "asymptotic analysis",
      "periodic dirichlet data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}