{
  "abstract": "We give a proof of optimal pointwise linear inviscid damping and vorticity depletion for a large class of spectrally stable shear flows $b(y)$ on the rectangular torus. This extends the linear inviscid estimates in \\cite{CJWZ25} for Kolmogorov flow $b(y) =\\cos y$ using completely different methods. Crucially, both methods remove an apparent logarithmic correction to the depletion and inviscid damping rates. Our method combines pointwise bounds for a parametrix with an explicit solution of a simpler inner problem which makes the removal of the logarithm clear.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08912",
  "author_total": 3,
  "authors": [
    {
      "name": "Rajendra Beekie"
    },
    {
      "name": "Shan Chen"
    },
    {
      "name": "Hao Jia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95ab5r6f26tk4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08912",
  "fulltext_url": null,
  "id": "95ab5r6f26tk4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08912",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7220949891",
  "pdf_url": "https://arxiv.org/pdf/2610.08912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95ab5r6f26tk4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows",
  "title_text": "Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/95ab5r6f26tk4",
  "venue": "arXiv",
  "versions": []
}