{
  "abstract": "We study the stability and temporal decay of solutions to the two-dimensional tropical climate model with Laplacian dissipation in both velocity equations and no thermal diffusion. For initial data in $H^s (\\mathbb{R}^2)$ ($s \\geq 1$) with sufficiently small $H^1$ norm, we establish a unique global solution satisfying uniform $H^s$ bounds and time-integrated estimates for the velocity and temperature. The smallness is independent of $s$, and the higher Sobolev norms of the initial data need not be small. Furthermore, without additional spatial integrability or negative-order regularity of the initial data, we prove that the $\\dot H^s (\\mathbb{R}^2)$ norms of the solutions are $o(t^{- s / 2})$ as $t \\to \\infty$. We also show that this decay rate is sharp: no additional decay factor tending to zero works for all such initial data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.10989",
  "author_total": 3,
  "authors": [
    {
      "name": "Hyunjin In"
    },
    {
      "name": "Dong-ha Kim"
    },
    {
      "name": "Junha Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88ep088hsk4vg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.10989",
  "fulltext_url": null,
  "id": "88ep088hsk4vg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.10989",
  "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/2611.10989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88ep088hsk4vg.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:34Z",
      "native_id": "2611.10989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.10989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Higher-order Sobolev stability and temporal decay estimate for the tropical climate model with small $H^1$ data",
  "title_text": "Higher-order Sobolev stability and temporal decay estimate for the tropical climate model with small H^1 data",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:34Z",
  "url": "https://research.draconitic.com/paper/88ep088hsk4vg",
  "venue": "arXiv",
  "versions": []
}