{
  "abstract": "Global existence of Leray-Hopf (type) weak solutions to the viscous primitive equations in two or three dimensions was established by Lions--Temam--Wang \\cite{Lions1,Lions2,Lions3,Lions4} in the 1990s; however, the corresponding uniqueness, no matter in two or three dimensions, has been a long standing open problem since then. In this paper, we solve this open problem in the two-dimensional case. Precisely, we prove the uniqueness of Leray-Hopf weak solutions, with arbitrary $L^2$ initial data, to the viscous primitive equations in a periodic channel, subject to impermeability and stress-free boundary conditions on the solid boundaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11339",
  "author_total": 4,
  "authors": [
    {
      "name": "Jinkai Li"
    },
    {
      "name": "Lintao Liu"
    },
    {
      "name": "Edriss S. Titi"
    },
    {
      "name": "Dong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0znsa5vv38my.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11339",
  "fulltext_url": null,
  "id": "e0znsa5vv38my",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11339",
  "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": "W7221067396",
  "pdf_url": "https://arxiv.org/pdf/2610.11339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0znsa5vv38my.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.11339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness of Leray-Hopf weak solutions to the two-dimensional viscous Primitive Equations",
  "title_text": "Uniqueness of Leray-Hopf weak solutions to the two-dimensional viscous Primitive Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/e0znsa5vv38my",
  "venue": "arXiv",
  "versions": []
}