{
  "abstract": "We consider a two-dimensional incompressible viscous fluid confined in a periodic channel between a fixed flat wall and a purely elastic periodic beam. For compatible initial fluid velocity in $H^1$, beam height in $H^3$, and beam velocity in $H^1$, with strictly positive initial height, we establish global existence and uniqueness of strong solutions. In particular, there is no contact of the beam and bottom, which is built on a uniform distance bound derived by the mechanical energy and fluid dissipation through a height-dependent degenerate elliptic regularization of the classical distance test. Combining tangential differentiation, a fractional estimate for the height, and a negative-order tangential estimate for the accelerations, we establish a global regularity estimate. Moreover, quadratic time-weighted estimates that quantify the higher regularity at positive times are justified. As a consequence, the work gives an affirmative answer to the problem proposed by Grandmont and Hillairet (Arch. Ration. Mech. Anal. 220(3): 1283--1333, 2016) of whether fluid dissipation alone is sufficient to derive the distance estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22090",
  "author_total": 1,
  "authors": [
    {
      "name": "Yadong Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1q9efwcqw52vk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22090",
  "fulltext_url": null,
  "id": "1q9efwcqw52vk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22090",
  "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": "W7222661538",
  "pdf_url": "https://arxiv.org/pdf/2610.22090",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1q9efwcqw52vk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22090",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22090"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global strong solutions without contact for a viscous fluid interacting with a purely elastic beam",
  "title_text": "Global strong solutions without contact for a viscous fluid interacting with a purely elastic beam",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1q9efwcqw52vk",
  "venue": "arXiv",
  "versions": []
}