{
  "abstract": "We study the three-dimensional primitive equations with full viscosity and horizontal thermal diffusion in bounded domains. We establish global well-posedness for admissible $H^1$ initial data and persistence of $H^2$ regularity on the flat-bottom cylinder. The higher regularity analysis combines fractional hydrostatic Stokes regularity with anisotropic estimates of the vertical transport. We also consider variable-depth domains with positive $h\\in C^3(\\overline M)$ and a diffusion operator adapted to the topography compatible with layers $z/h(x,y)=\\mathrm{constant}$. This operator reduces to $Δ_H$ at constant depth and generally differs from the Cartesian horizontal Laplacian over a varying bottom. Its weighted formulation yields global strong solutions for admissible $H^1$ data. Persistence of $H^2$ regularity is proved under the additional assumption $\\partial_νh=0$ on $\\partial M$, where $ν$ is the outward horizontal unit normal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14555",
  "author_total": 2,
  "authors": [
    {
      "name": "Qimin Wang"
    },
    {
      "name": "Mohammed Ziane"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezvt1xb05hc1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14555",
  "fulltext_url": null,
  "id": "ezvt1xb05hc1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14555",
  "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": "W7221813896",
  "pdf_url": "https://arxiv.org/pdf/2610.14555",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezvt1xb05hc1p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14555",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14555"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion",
  "title_text": "Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ezvt1xb05hc1p",
  "venue": "arXiv",
  "versions": []
}