{
  "abstract": "We formalize in Lean 4 the Galerkin construction of global Leray--Hopf weak solutions for the unforced two-dimensional Navier--Stokes equations on arbitrary bounded open domains with no-slip boundary conditions. For every initial datum in the solenoidal \\(L^2\\) velocity space, the solution has a weakly continuous velocity path, satisfies the weak equation locally in time, and obeys the energy inequality at every time. For rectangles, we also formalize finite-horizon solutions with continuous forcing in the dual energy space. The development includes divergence-free graph spaces, compact spectral coordinates, transport cancellation, Ladyzhenskaya estimates, and simultaneous space--time compactness. The abstract Hilbert-space results apply to evolution equations with a compact energy-to-velocity embedding and a skew trilinear nonlinearity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33033",
  "author_total": 1,
  "authors": [
    {
      "name": "Weinan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cm3gwm820mmw9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33033",
  "fulltext_url": null,
  "id": "cm3gwm820mmw9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33033",
  "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",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214749320",
  "pdf_url": "https://arxiv.org/pdf/2609.33033",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cm3gwm820mmw9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33033",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33033"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Formalization of the Galerkin Construction for the Two-Dimensional Navier--Stokes Equations in Lean",
  "title_text": "Formalization of the Galerkin Construction for the Two-Dimensional Navier--Stokes Equations in Lean",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cm3gwm820mmw9",
  "venue": "arXiv",
  "versions": []
}