{
  "abstract": "We prove a local Hartman-Grobman theorem at zero for the unforced Navier-Stokes equation on the three-dimensional torus in the strong topology of $H^s$ for every $s>7/2$. More precisely, we construct a homeomorphism between open positively invariant neighborhoods of zero that conjugates the Navier-Stokes semiflow to the heat semigroup. We develop an infinite-dimensional boundary-time scheme built on a nested hierarchy of exact asymptotic dynamical factors. Their fiber geometry yields Sobolev block coordinates with autonomous finite-dimensional factor systems, on which boundary-time topological conjugacies can be constructed at every finite level and then assembled on a common neighborhood into the desired $H^s$ conjugacy. The infinite-dimensional assembly relies on new spectral estimates for the divergence-free transport structure, which control derivative loss and the blockwise tails of the finite-level conjugacies and their inverses without an additional spectral-gap assumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08058",
  "author_total": 3,
  "authors": [
    {
      "name": "Rongchang Liu"
    },
    {
      "name": "Kening Lu"
    },
    {
      "name": "Lin Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b92d7me8hk3fe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08058",
  "fulltext_url": null,
  "id": "b92d7me8hk3fe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08058",
  "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"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7220991442",
  "pdf_url": "https://arxiv.org/pdf/2610.08058",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b92d7me8hk3fe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08058",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08058"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A Hartman-Grobman Theorem for the Navier-Stokes Equation on $\\mathbb T^3$",
  "title_text": "A Hartman-Grobman Theorem for the Navier-Stokes Equation on 𝕋^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/b92d7me8hk3fe",
  "venue": "arXiv",
  "versions": []
}