{
  "abstract": "In this paper, we study the continuous dependence of solutions to the three-dimensional incompressible anisotropic Navier-Stokes equations $(ANS)$ with initial data in the critical space $\\dot{B}^{0,\\frac12}$. We prove that the data-to-solution map is continuous in this setting. Due to the critical regularity of the problem, the classical Bona-Smith argument \\cite{BoSm} (see also the abstract result \\cite{ABITZ}) does not appear to apply because a key ingredient (the Lipschitz continuity at lower regularity) does not appear to hold. As a consequence, we develop a new direct Fourier-weighted method within the Besov framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14304",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicolas Burq"
    },
    {
      "name": "Ning Liu"
    },
    {
      "name": "Ping Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c84c5e5vcaps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14304",
  "fulltext_url": null,
  "id": "5c84c5e5vcaps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14304",
  "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": "W7213312128",
  "pdf_url": "https://arxiv.org/pdf/2609.14304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c84c5e5vcaps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the stability of solutions to the 3-D anisotropic Navier-Stokes equations in the critical space",
  "title_text": "On the stability of solutions to the 3-D anisotropic Navier-Stokes equations in the critical space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5c84c5e5vcaps",
  "venue": "arXiv",
  "versions": []
}