{
  "id": "2108.11192",
  "version": "v1",
  "published": "2021-08-25T11:42:34.000Z",
  "updated": "2021-08-25T11:42:34.000Z",
  "title": "Enhanced dissipation and Taylor dispersion in higher-dimensional parallel shear flows",
  "authors": [
    "Thierry Gallay",
    "Michele Coti Zelati"
  ],
  "comment": "26 pages, no figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity $\\nu$, which is assumed to be small, and the wave number $k$ in the streamwise direction, which can take arbitrary values. Under generic assumptions on the shear velocity, we obtain optimal decay estimates for large times, both in the enhanced dissipation regime $\\nu \\ll |k|$ and in the Taylor dispersion regime $|k| \\ll \\nu$. Our results can be deduced from resolvent estimates using a quantitative version of the Gearhart-Pr\\\"uss theorem, or can be established more directly via the hypocoercivity method. Both approaches are implemented in the present example, and their relative efficiency is compared.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-25T11:42:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35H10",
      "47B44",
      "76E05"
    ],
    "keywords": [
      "higher-dimensional parallel shear flows",
      "enhanced dissipation",
      "arbitrary space dimension",
      "optimal decay estimates",
      "taylor dispersion regime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}