{
  "abstract": "Let $Ω$ be a bounded $C^1$ domain in $\\mathbb{R}^d$, $d\\geq2$. We establish vector-valued resolvent estimates for the Dirichlet Stokes system in $L^q(Ω;\\ell^2)$ for every $1<q<\\infty$. The estimates are uniform in the number and choice of spectral parameters in any fixed sector avoiding the negative real axis. These estimates imply that the Stokes operator is $\\mathcal R$-sectorial of angle zero and has maximal $L^r$-regularity for every $1<r<\\infty$. Our proof builds on the perturbation approach of Geng and Shen, with a different half-space argument to handle independently varying spectral parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04464",
  "author_total": 1,
  "authors": [
    {
      "name": "Su Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3km1rwdydzymj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04464",
  "fulltext_url": null,
  "id": "3km1rwdydzymj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04464",
  "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/2611.04464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3km1rwdydzymj.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Maximal regularity for the Stokes operator in bounded $C^1$ domains",
  "title_text": "Maximal regularity for the Stokes operator in bounded C^1 domains",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/3km1rwdydzymj",
  "venue": "arXiv",
  "versions": []
}