{
  "abstract": "In this paper, we are concerned with space-time derivative estimates of solutions to the fractional Navier-Stokes equations. It is shown that $Λ^{nα}u^{(m)}_{t} \\in L^{\\frac{2(6α-5)}{4mα+2nα+4 α-5}}~~~~~~~(0,T; L^{2}(\\mathbb{R}^{3}))$ and $ Λ^{n }u^{(m)}_{t} \\in L^{\\frac{2(6α-5)}{4mα+2n +4 α-5}}~~~~~(0,T; L^{2}(\\mathbb{R}^{3}))$. This generalizes a priori bounds for the classical Navier-Stokes system by Duff in [7, Acta Math. 164, 1990] and Boutros and Gibbon's spatial derivative estimates in [1, Nonlinearity 37, 2024]. In addition, we derive that $ u \\in L^{\\frac{q}{q-3}}~~(0,T;L^{q} (\\mathbb{R}^{3}))$ with $ 6\\leq q\\leq\\infty $ and $Λ^{k}u \\in L^{\\frac{q}{ q(k+1)-3}}~~~(0,T;L^{q} (\\mathbb{R}^{3})) $ with $k\\geq1, 2\\leq q\\leq\\infty $ in the standard Navier-Stokes equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12864",
  "author_total": 4,
  "authors": [
    {
      "name": "Yanqing Wang"
    },
    {
      "name": "Wei Wei"
    },
    {
      "name": "Gang Wu"
    },
    {
      "name": "Daoguo Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kvyrdk1x2yxh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12864",
  "fulltext_url": null,
  "id": "8kvyrdk1x2yxh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12864",
  "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": "W7212635334",
  "pdf_url": "https://arxiv.org/pdf/2609.12864",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kvyrdk1x2yxh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12864",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12864"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On space-time derivative estimates for the fractional Navier-Stokes equations",
  "title_text": "On space-time derivative estimates for the fractional Navier-Stokes equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/8kvyrdk1x2yxh",
  "venue": "arXiv",
  "versions": []
}