{
  "abstract": "In this paper, we establish two improved Liouville-type theorems for the three-dimensional stationary tropical climate model without imposing any temperature assumptions. Compared with previous results, we achieve significant improvements on the growth assumptions imposed on $u$, $v$ and $\\nabla v$. Owing to the special structure inherent to the equations, we fully exploit the $L^2$-estimate for the oscillation of the temperature, refined interpolation techniques and an iteration argument to establish a Liouville-type theorem under flexible and relaxed power-law growth conditions. As an interesting consequence, we obtain the triviality of solutions under the integrability conditions imposed only on $(u,\\nabla v)$ or $(\\nabla u,\\nabla v)$. Furthermore, by developing a systematic framework to handle the energy function associated with the non-trivial solutions and with the aid of delicate ODE analysis and a contradiction argument, we refine our Liouville-type theorem by introducing logarithmic corrections to the growth rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13149",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhibing Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/epxkb6ggy41bv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13149",
  "fulltext_url": null,
  "id": "epxkb6ggy41bv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13149",
  "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|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7203455813",
  "pdf_url": "https://arxiv.org/pdf/2608.13149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/epxkb6ggy41bv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.13149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions",
  "title_text": "Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/epxkb6ggy41bv",
  "venue": "arXiv",
  "versions": []
}