{
  "abstract": "We investigate the steady configurations supported by the inviscid two-dimensional Boussinesq equations in the periodic channel. We show steady laminar velocity fields (closed non-contractible fluid trajectories) coupled to non-decreasing density stratifications are necessarily stratified shear flows. The direction of density monotonicity along level sets is in fact fundamental: in striking contrast with the Euler equations, we exhibit laminar non-stagnant non-shear stationary solutions in the periodic channel. We also provide distinct flexibility and rigidity results (laminar persistence or appearance of islands for nearby non-shear solutions) close to stratified shear flows according to their stagnation points. As a by-product of our analysis, we establish a uniform Crandall-Rabinowitz bifurcation theorem that might be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40334",
  "author_total": 3,
  "authors": [
    {
      "name": "Marc Nualart"
    },
    {
      "name": "Jaemin Park"
    },
    {
      "name": "Javier Peñafiel-Tomás"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1q8b3gh6br100.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40334",
  "fulltext_url": null,
  "id": "1q8b3gh6br100",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40334",
  "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"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40334",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1q8b3gh6br100.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40334",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40334"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Stationary Structures of the Boussinesq equations",
  "title_text": "Stationary Structures of the Boussinesq equations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1q8b3gh6br100",
  "venue": "arXiv",
  "versions": []
}