{
  "abstract": "We study the nonlinear stability of the quadratic plane Poiseuille flow $U(y)=(y^2,0)$ for the two-dimensional incompressible Navier--Stokes equations on $\\mathbb T\\times\\mathbb R$. We prove that for initial perturbations of size $O(ν^{2/3})$ in a $ν$-dependent weighted Sobolev space, the flow is globally nonlinearly stable. In particular, the nonzero streamwise modes experience enhanced dissipation and decay exponentially on the characteristic time scale $O(ν^{-1/2})$, while the zero mode remains uniformly controlled. Thus, in this weighted Sobolev topology, \\(O(ν^{2/3})\\) is a sufficient stability scale without logarithmic loss.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35185",
  "author_total": 3,
  "authors": [
    {
      "name": "Tao Liang"
    },
    {
      "name": "Cuili Zhai"
    },
    {
      "name": "Xiaoping Zhai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/evnjwkrfmr20t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35185",
  "fulltext_url": null,
  "id": "evnjwkrfmr20t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35185",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214787390",
  "pdf_url": "https://arxiv.org/pdf/2609.35185",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/evnjwkrfmr20t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35185",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35185"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Enhanced dissipation and stability threshold for the Navier--Stokes equations near Poiseuille flow",
  "title_text": "Enhanced dissipation and stability threshold for the Navier--Stokes equations near Poiseuille flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/evnjwkrfmr20t",
  "venue": "arXiv",
  "versions": []
}