{
  "abstract": "We study an inextensible open filament with free ends in a planar Stokes fluid. The system reduces to a third-order nonlocal curvature equation coupled to an elliptic equation for the tension. We prove local well-posedness for nearly critical initial data in supported Sobolev spaces $\\widetilde H^s$, $-1/2<s\\le0$, satisfying the arc-chord condition. For positive times, we prove improved Sobolev regularity and derive a $d^{3/2}$-type expansion at each free end using Wiener--Hopf factorization, where $d$ denotes the distance to that endpoint. We further prove global existence and exponential convergence to a straight filament for sufficiently small initial data and for finite-energy initial data satisfying $E(0)<π^2/4$. The finite-energy result follows from an energy identity and a geometric estimate relating the bending energy to the arc-chord constant. More generally, any finite-time breakdown must be accompanied by loss of the arc-chord condition, while every global solution either converges exponentially to a straight filament or has arc-chord constants tending to zero along a sequence of times tending to infinity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10480",
  "author_total": 1,
  "authors": [
    {
      "name": "Han Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ep0ftw6v505s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10480",
  "fulltext_url": null,
  "id": "0ep0ftw6v505s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10480",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7212125097",
  "pdf_url": "https://arxiv.org/pdf/2609.10480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ep0ftw6v505s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Open Inextensible Filaments in Planar Stokes Flow: Well-Posedness, Endpoint Asymptotics, and Straightening",
  "title_text": "Open Inextensible Filaments in Planar Stokes Flow: Well-Posedness, Endpoint Asymptotics, and Straightening",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/0ep0ftw6v505s",
  "venue": "arXiv",
  "versions": []
}