{
  "titles": [
    {
      "title": "Mixing for generic rough shear flows"
    }
  ],
  "creators": [
    {
      "name": "Galeati, Lucio",
      "nameType": "Personal",
      "familyName": "Galeati",
      "givenName": "Lucio"
    },
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2021,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "2",
  "url": "https://arxiv.org/abs/2107.12115v2",
  "dates": [
    {
      "date": "2021-07-26",
      "dateType": "Issued"
    },
    {
      "date": "2023-06-21",
      "dateType": "Available"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math.AP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "Creative Commons Attribution 4.0 International",
      "rightsIdentifier": "cc-by-4.0",
      "rightsUri": "http://creativecommons.org/licenses/by/4.0/",
      "rightsIdentifierScheme": "SPDX"
    }
  ],
  "descriptions": [
    {
      "description": "We study mixing and diffusion properties of passive scalars driven by $generic$ rough shear flows. Genericity is here understood in the sense of prevalence and (ir)regularity is measured in the Besov-Nikolskii scale $B^{\\alpha}_{1, \\infty}$, $\\alpha \\in (0, 1)$. We provide upper and lower bounds, showing that in general inviscid mixing in $H^{1/2}$ holds sharply with rate $r(t) \\sim t^{1/(2 \\alpha)}$, while enhanced dissipation holds with rate $r(\\nu) \\sim \\nu^{\\alpha / (\\alpha+2)}$. Our results in the inviscid mixing case rely on the concept of $\\rho$-irregularity, first introduced by Catellier and Gubinelli (Stoc. Proc. Appl. 126, 2016) and provide some new insights compared to the behavior predicted by Colombo, Coti Zelati and Widmayer (arXiv:2009.12268, 2020).",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:2107.12115v2",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.2107.12115",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}