{
  "abstract": "In this paper, we present the space-time derivative estimates of solutions to the MHD equations. It is a generalization of a priori bounds for the classical Navier-Stokes system by Duff in \\cite[Acta Math. 164, 1990]{[Duff]} and gives an affirmative answer to a question proposed by Zheligovsky in \\cite[Mathematics. 9, 2021]{[Zheligovsky]}. In addition, we show that $u, B \\in L^{\\f{q}{q-3}}(0,T;L^{q} (\\mathbb{R}^{3}))$ with $6\\leq q\\leq\\infty $ and $ D ^{k}u, D ^{k}B \\in L^{\\f{q}{ q(k+1)-3}}(0,T;L^{q} (\\mathbb{R}^{3}))$ for $k\\geq1, 2\\leq q\\leq\\infty$ in this system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12901",
  "author_total": 4,
  "authors": [
    {
      "name": "Yanqing Wang"
    },
    {
      "name": "Wei Wei"
    },
    {
      "name": "Gang Wu"
    },
    {
      "name": "Yulin Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgjtteanzn1b0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12901",
  "fulltext_url": null,
  "id": "bgjtteanzn1b0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12901",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.12901",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgjtteanzn1b0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12901",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12901"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On space-time derivative estimates for the magnetohydrodynamic equations",
  "title_text": "On space-time derivative estimates for the magnetohydrodynamic equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/bgjtteanzn1b0",
  "venue": "arXiv",
  "versions": []
}