{
  "abstract": "We study solutions to the Navier-Stokes equations in the class $L^\\infty_t C^α_x$. Landau and Lifshitz [LL87] predicted that the Eulerian and Lagrangian temporal structure functions for turbulence exhibit $1/3$ and $1/2$ scaling laws, respectively. These laws were justified for the Euler equations in [Ise23,Ise25], assuming the spatial structure functions satisfies a $1/3$ scaling law. We demonstrate them in a viscous setting by proving that the $C^α_{t,x}$-norm of the solution and the $C^{1/(1-α)}$-norm of any fluid trajectory can be estimated by the $L^\\infty_tC^α_x$-norm independently of the viscosity parameter $ν>0$, for times bounded away from zero by a positive power of $ν$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.22006",
  "author_total": 1,
  "authors": [
    {
      "name": "Ming-Yuan Chang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38mn4wmfqnefp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.22006",
  "fulltext_url": null,
  "id": "38mn4wmfqnefp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.22006",
  "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": "W7162086615",
  "pdf_url": "https://arxiv.org/pdf/2605.22006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38mn4wmfqnefp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2605.22006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.22006"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Hölder estimate for the trajectories of the Navier-Stokes equations",
  "title_text": "A Hölder estimate for the trajectories of the Navier-Stokes equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/38mn4wmfqnefp",
  "venue": "arXiv",
  "versions": []
}