{
  "abstract": "We prove uniqueness of solutions to the Navier-Stokes equations in the space \\[ L^p\\bigl([0,T],\\widetilde{L}^{3,\\infty}(\\mathbb{R}^3)\\bigr) \\cap C\\bigl([0,T],B^{-1,\\infty}_{\\infty}(\\mathbb{R}^3)\\bigr), \\qquad p>2, \\] where $\\widetilde{L}^{3,\\infty}(\\mathbb{R}^3)$ denotes the closure of the Schwartz space $\\mathcal{S}(\\mathbb{R}^3)$ in the Lorentz space $L^{3,\\infty}(\\mathbb{R}^3)$. Moreover, we prove that any solution $u$ in this class, if it exists, is smooth for positive time, namely, $u\\in C^\\infty((0,T]\\times \\mathbb{R}^3)$. In addition, we establish precise estimates for the behavior of $u(t)$ as $t\\to0^+ $ in various Banach spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14688",
  "author_total": 1,
  "authors": [
    {
      "name": "Ramzi May"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/92gms66m4an1n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14688",
  "fulltext_url": null,
  "id": "92gms66m4an1n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14688",
  "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/2609.14688",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/92gms66m4an1n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14688",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14688"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the uniqueness and the regularity of solutions to the Navier Stokes in the Lorentz space $L^{3,\\infty}(\\mathbb{R}^3)$",
  "title_text": "On the uniqueness and the regularity of solutions to the Navier Stokes in the Lorentz space L^3,∞(ℝ^3)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/92gms66m4an1n",
  "venue": "arXiv",
  "versions": []
}