{
  "abstract": "Consider a $d$-sphere $\\mathbb{S}^d$ and denote by $Γ(T\\mathbb{S}^d)$ the set of all vector fields on $\\mathbb{S}^d$. We study the Navier-Stokes equations (NSE): $$ \\partial_t u + \\nabla_u u + grad π= \\mathbfΔ u + \\operatorname{div} f(\\cdot, t);\\, \\operatorname{div} u=0,$$ for the vector field $u(\\cdot, t)\\in Γ(T\\mathbb{S}^d)$, where $\\mathbfΔ$ denotes the Ebin-Marsden Laplace operator defined by $\\mathbfΔ u= \\operatorname{div} (\\nabla u + \\nabla u^t)^{\\sharp}$, and $\\operatorname{div} f(\\cdot, t)$ is the periodic external force. We investigate the Navier-Stokes equations in the framework of $L^p$-spaces over vector fields on $\\mathbb{S}^d$ and prove the existence and uniqueness of a periodic solution to such equations. Moreover, exploiting the distribution of eingenvalues of Ebin-Marsden Laplace operator we show the existence of an inertial manifold for solutions around that solution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11084",
  "author_total": 2,
  "authors": [
    {
      "name": "Thi Ngoc Ha Vu"
    },
    {
      "name": "Thieu Huy Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qcddxv9b6rdm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11084",
  "fulltext_url": null,
  "id": "6qcddxv9b6rdm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11084",
  "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": "W7221143991",
  "pdf_url": "https://arxiv.org/pdf/2610.11084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qcddxv9b6rdm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Periodicity and Inertial Manifolds for Navier-Stokes Flows on $d$-Spheres",
  "title_text": "Periodicity and Inertial Manifolds for Navier-Stokes Flows on d-Spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/6qcddxv9b6rdm",
  "venue": "arXiv",
  "versions": []
}