{
  "abstract": "This paper is devoted to the well-posedness of classical Prandtl equations in a finite order Sobolev space. For a initial data with degenerate critical points and general outflow, we obtain the local-in-time existence and uniqueness of the solution to the Prandtl equations in a Sobolev space, by introducing a new iteration scheme and linear cancelation. This result shows that Oleinik's monotonicity condition is not a necessary condition for the Prandtl equations to be well-posed in Sobolev spaces and provides evidence to demonstrate that zero shear stress does not necessarily lead to boundary layer separation in two-dimensional unsteady boundary layers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10936",
  "author_total": 2,
  "authors": [
    {
      "name": "Shi-Yong Zhu"
    },
    {
      "name": "Ya-Guang Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eb7xcpk372m1f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10936",
  "fulltext_url": null,
  "id": "eb7xcpk372m1f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10936",
  "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": "W7212270455",
  "pdf_url": "https://arxiv.org/pdf/2609.10936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eb7xcpk372m1f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10936"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points",
  "title_text": "Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/eb7xcpk372m1f",
  "venue": "arXiv",
  "versions": []
}