{
  "abstract": "This paper is devoted to the global dynamics of a nonlocal Lagrangian-averaged Navier-Stokes-$α$ (LANS-$α$)-type system (also known as the viscous Euler-Poincaré system) in one, two, and three spatial dimensions. In the unforced periodic setting with zero mean, we establish global well-posedness for the initial-value problem and prove that the corresponding solution semigroup is dissipative and possesses a compact global attractor consisting of the singleton $\\{0\\}$. Furthermore, we obtain the following global-in-time algebraic asymptotic stability estimate: \\[ \\|u(t,\\cdot)\\|_{H^3}\\lesssim t^{-1/2},\\qquad \\forall\\, t>0, \\] which is derived from higher-order energy inequalities combined with a uniform Gronwall-type argument. Our results provide a complete description of the long-time behavior of the unforced periodic dynamics for this nonlocal LANS-$α$-type system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25661",
  "author_total": 3,
  "authors": [
    {
      "name": "Chunxia Guan"
    },
    {
      "name": "Kai Yan"
    },
    {
      "name": "Qianyuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kq67wfxaw84y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25661",
  "fulltext_url": null,
  "id": "8kq67wfxaw84y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25661",
  "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/2609.25661",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kq67wfxaw84y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25661",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25661"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global dynamics and asymptotic stability for a nonlocal LANS-$α$-type system",
  "title_text": "Global dynamics and asymptotic stability for a nonlocal LANS-α-type system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/8kq67wfxaw84y",
  "venue": "arXiv",
  "versions": []
}