{
  "abstract": "Focusing on the pullback asymptotic behavior exhibited by the system, this paper studies the three-dimensional (3D) non-autonomous Boussinesq equations with fractional Laplacian. For $ α> \\frac{5}{4} $ and $ β> \\frac{5}{8} $, by adopting the $ \\ell $-trajectory method introduced in \\cite{MP2002}, we demonstrate the existence of both a finite-dimensional pullback attractor and a pullback exponential attractor for the process $ \\{L(t, τ)\\}_{t \\geq τ} $ that corresponds to \\cref{eq0101} in the phase space $ X_{\\ell} $. Furthermore, we establish the existence of a pullback exponential attractor for the process $ \\{U(t, τ)\\}_{t \\geq τ} $ within the original phase space $ H_σ^α(Ω) \\times H^β(Ω) $.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18114",
  "author_total": 4,
  "authors": [
    {
      "name": "Tong Kou"
    },
    {
      "name": "Hui Liu"
    },
    {
      "name": "Xiuqing Wang"
    },
    {
      "name": "Jie Xin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1ms6nt3a6etd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18114",
  "fulltext_url": null,
  "id": "a1ms6nt3a6etd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18114",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18114",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1ms6nt3a6etd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18114",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18114"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Pullback exponential attractors for 3D non-autonomous Boussinesq equations with fractional Laplacian",
  "title_text": "Pullback exponential attractors for 3D non-autonomous Boussinesq equations with fractional Laplacian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/a1ms6nt3a6etd",
  "venue": "arXiv",
  "versions": []
}