{
  "abstract": "Exact periodic solutions of the unforced incompressible Navier-Stokes equations require the convective field to be a pure gradient, absorbed into the pressure; for the cyclic trigonometric families studied previously this occurs only at isolated phases and, over the range so far classified, only at n = 3 and 4. The forced problem, we show, admits an exact construction for every phase vector and every n >= 3. For an n-parameter family of two-term cyclic fields, solenoidal and a Laplacian eigenfunction, the transverse part U^0 of its convective field serves as the body force, giving a closed-form solution with velocity, pressure and force explicit. We prove closed forms for the pressure and for both magnitudes, in every dimension and with no upper bound on n: the forcing is never trivial, and the L^2 magnitude of U^0 stands to that of the whole convective field in the constant ratio 2*sqrt(2)/3, whatever the dimension, phase or units. The forcing does no net work, so the kinetic energy decays purely viscously at arbitrary Reynolds number, giving an exact benchmark in any dimension. A numerical study of vorticity concentration at zero applied work uses it as a reference, and shows that apparent saturation can be a resolution artefact.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38210",
  "author_total": 1,
  "authors": [
    {
      "name": "R. K. Michael Thambynayagam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d2tp4a918564.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38210",
  "fulltext_url": null,
  "id": "5d2tp4a918564",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38210",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7215080710",
  "pdf_url": "https://arxiv.org/pdf/2609.38210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d2tp4a918564.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2609.38210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38210"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Exact Periodic Solutions of the Forced Incompressible Navier-Stokes Equations in Arbitrary Dimensions",
  "title_text": "Exact Periodic Solutions of the Forced Incompressible Navier-Stokes Equations in Arbitrary Dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/5d2tp4a918564",
  "venue": "arXiv",
  "versions": []
}