{
  "abstract": "By refining the approach developed in \\cite{AGH-2015, GS2026a}, we establish resolvent estimates in $L^p_σ(Ω)$ for the Stokes operator in a bounded Lipschitz domain $Ω$ in $\\R^3$ for any $(3/2)-\\e< p\\le \\infty$, where $\\e>0$ depends on $Ω$. As a consequence, the Stokes operator generates a uniformly bounded analytic semigroup in $L^p_σ(Ω)$. The results are particularly surprising, as it is long believed that the $L^p$ resolvent estimates in three-dimensional Lipschitz domains may fail for large $p$. In the Appendices we prove a theorem on interpolation between $L^2_σ(Ω)$ and $L^\\infty_σ(Ω)$. Given $1< p< \\infty$ and a bounded Lipschitz domain $Ω$ in $\\R^d, d\\ge 2$, we show that the resolvent estimate cannot hold in $L^p(Ω; \\C^d)$ unless the Helmholtz projection is bounded on $L^p(Ω; \\C^d)$. This explains the counter-example constructed in \\cite{Deuring-2001}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02552",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhongwei Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ehtmzqx39j4c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02552",
  "fulltext_url": null,
  "id": "2ehtmzqx39j4c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02552",
  "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": "W7207718240",
  "pdf_url": "https://arxiv.org/pdf/2609.02552",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ehtmzqx39j4c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.02552",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02552"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Resolvent Estimates for the Stokes Operator in a Three-Dimensional Lipschitz Domain",
  "title_text": "Resolvent Estimates for the Stokes Operator in a Three-Dimensional Lipschitz Domain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2ehtmzqx39j4c",
  "venue": "arXiv",
  "versions": []
}