{
  "abstract": "We establish quantitative $L^1$ instability for the two-dimensional Navier--Stokes equations near a self-similar three-vortex collapse as viscosity tends to zero. For every $0<γ<\\frac12$ and $t_0\\in(0,1)$, we construct solutions that are $O(ν^{1-γ})$-close in $L^1(\\mathbb{R}^2)$ at $t_0$ but exhibit order-one $L^1$ separation in a shrinking neighborhood of the collapse point at times approaching collapse as $ν\\to0$. By time translation, we also obtain pairs of solutions with initial $L^1$ distance $O(ν^{1-γ})$ that develop order-one separation at a fixed positive time. In both constructions, the solutions have the same viscosity and total circulation and are uniformly bounded in $L^1(\\mathbb{R}^2)$. The proof exploits the amplification of small time delays, the fast speed of the vortex centers near collapse, together with sharp inviscid approximation estimates for the Navier--Stokes equations established in~\\cite{Ga11,NguyenCollapse}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01433",
  "author_total": 1,
  "authors": [
    {
      "name": "Trinh T. Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0bfxdr6w2r2sw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01433",
  "fulltext_url": null,
  "id": "0bfxdr6w2r2sw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01433",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0bfxdr6w2r2sw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01433"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^1$ amplification near a self-similar vortex collapse in 2D Navier-Stokes",
  "title_text": "L^1 amplification near a self-similar vortex collapse in 2D Navier-Stokes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0bfxdr6w2r2sw",
  "venue": "arXiv",
  "versions": []
}