{
  "abstract": "This paper addresses the global existence and large-time decay of solutions to the two-dimensional compressible Prandtl equations in Sobolev spaces. We study small perturbations around a monotone shear flow and establish global weighted Sobolev estimates together with precise time-decay rates for the solutions. The main difficulties are that the normal velocity causes a loss of one tangential derivative, the variable density gives rise to nonstandard boundary and shear-flow coupling terms, and the global-in-time argument requires sufficiently strong decay to close the time-weighted energy estimates. To overcome these difficulties, we combine the cancellation method introduced by Masmoudi and Wong~\\cite{MW2015} with the good-quantity approach developed by Paicu and Zhang~\\cite{PZ2021}, together with weighted shear-flow estimates and a careful treatment of the natural boundary structure. Under suitable assumptions on the density perturbation, the shear flow, and the function $f(t)$ describing the outer tangential flow, we prove the global-in-time well-posedness of solutions in weighted Sobolev spaces. In this sense, the present result may be viewed as a Sobolev-space counterpart of the recent analytic-framework result obtained by Chen, Huang and Li (J. Funct. Anal. 286 (2024), 110322)~\\cite{CHL2024} for the two-dimensional compressible Prandtl-type equations, while requiring a weaker time-decay assumption on the density perturbation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01925",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuming Qin"
    },
    {
      "name": "Junchen Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4aejzrb3y3xxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01925",
  "fulltext_url": null,
  "id": "4aejzrb3y3xxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01925",
  "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/2611.01925",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4aejzrb3y3xxn.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01925",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01925"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global existence and decay estimates of solutions for the compressible Prandtl type equations in Sobolev spaces",
  "title_text": "Global existence and decay estimates of solutions for the compressible Prandtl type equations in Sobolev spaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/4aejzrb3y3xxn",
  "venue": "arXiv",
  "versions": []
}