{
  "abstract": "We justify the anelastic approximation and establish a convergence rate for local strong solutions to the isentropic compressible Navier-Stokes equations in a three-dimensional bounded domain, with ill-prepared initial data and vorticity-slip boundary conditions. When the Mach and Froude numbers vanish at the same rate $ε$, the system converges to an anelastic system with nonconstant hydrostatic density. Compared with the incompressible limit, the balance between singular pressure and gravity generates a variable-coefficient acoustic operator and additional commutators. To overcome these difficulties, we introduce the pressure perturbation adapted to the hydrostatic balance and establish weighted acoustic and vorticity estimates, yielding uniform-in-$ε$ estimates. We then use the weighted Helmholtz decomposition and time-averaging technique to prove the strong convergence of solenoidal component of the momentum and obtain an error bound controlled by $ε$ and the initial error in the projected momentum. Our analysis reveals the weighted cancellation mechanism that applies to singular limits around a class of nonconstant equilibria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02831",
  "author_total": 2,
  "authors": [
    {
      "name": "Yaobin Ou"
    },
    {
      "name": "Ping Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3wvzwj8zrnn3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02831",
  "fulltext_url": null,
  "id": "d3wvzwj8zrnn3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02831",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3wvzwj8zrnn3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The anelastic approximation and convergence rate for the compressible Navier-Stokes equations with ill-prepared data in bounded domains",
  "title_text": "The anelastic approximation and convergence rate for the compressible Navier-Stokes equations with ill-prepared data in bounded domains",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d3wvzwj8zrnn3",
  "venue": "arXiv",
  "versions": []
}