{
  "abstract": "In this paper we consider the Navier-Stokes equations in exterior domains of $\\mathbb{R}^n$, $n\\geq 3$, with a periodically in time moving boundary $\\partialΩ(t)$ and external force $f(t)$. For this case we prove the existence of a locally unique mild time periodic solution in weighted function spaces with radially symmetric Muckenhoupt weights. The solutions split into a stationary part controlled by potential theoretic estimates and a purely oscillatory part constructed as mild solution via analytic semigroup theory. To deal with perturbation terms of even second order - coming from a coordinate transform and the moving boundary - in weighted, homogeneous Sobolev spaces a maximal $L^1$ type regularity estimate will be used in weighted Lorentz spaces. To control the convective term an $\\mathcal H^\\infty$-calculus in weighted spaces of the Stokes operator, its $BIP$ property and embedding estimates of fractional powers are exploited, see a recent paper by the authors: The Stokes operator on exterior domains in homogeneous weighted function spaces: From weak theory to $\\mathscr H^\\infty$-calculus to fractional domains (2025).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28999",
  "author_total": 2,
  "authors": [
    {
      "name": "Reinhard Farwig"
    },
    {
      "name": "Kazuyuki Tsuda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8eja020xwm5r3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28999",
  "fulltext_url": null,
  "id": "8eja020xwm5r3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28999",
  "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": "W7204867161",
  "pdf_url": "https://arxiv.org/pdf/2608.28999",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8eja020xwm5r3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28999",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28999"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Time periodic problem of the Navier-Stokes equations in an exterior domain with periodically moving boundary",
  "title_text": "Time periodic problem of the Navier-Stokes equations in an exterior domain with periodically moving boundary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8eja020xwm5r3",
  "venue": "arXiv",
  "versions": []
}