{
  "abstract": "We prove global existence of finite-energy renormalized weak solutions to the 2D isothermal compressible Navier--Stokes equations in bounded $C^2$ domains with no-slip boundary conditions. The initial data are arbitrary in the natural energy class, allowing vacuum and unbounded density. This resolves the isothermal endpoint $γ=1$ of the classical 2D finite-energy renormalized existence theory for power-law pressures. We develop a new endpoint compactness argument based on a truncation-independent integrable bound for centered density oscillations. This argument yields strong $L^1$ compactness of the approximating densities at the natural energy level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12387",
  "author_total": 1,
  "authors": [
    {
      "name": "Cheng Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2011abvwr6m2y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12387",
  "fulltext_url": null,
  "id": "2011abvwr6m2y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12387",
  "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": "W7221072918",
  "pdf_url": "https://arxiv.org/pdf/2610.12387",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2011abvwr6m2y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12387",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12387"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Endpoint Compactness and Finite-Energy Weak Solutions for the 2D Isothermal Compressible Navier-Stokes",
  "title_text": "Endpoint Compactness and Finite-Energy Weak Solutions for the 2D Isothermal Compressible Navier-Stokes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/2011abvwr6m2y",
  "venue": "arXiv",
  "versions": []
}