{
  "abstract": "Exact periodic solutions of the incompressible Navier-Stokes equations arise when the convective field is a pure gradient and can be absorbed into the pressure. We construct solutions outside this class, in arbitrary spatial dimension, by an iteration in which each step solves a linear diffusion problem forced by the transverse part of the preceding convective field. The construction is dimension-independent, and for a cyclic family of initial fields the first two iterates are available in closed form. Carried out numerically in three dimensions, the iteration converges: at Re = 10 successive iterates contract with an observed factor 0.43 and the limit is a fixed point of the discretised map to a relative defect of 8.2 x 10^-5. The observed factor exceeds unity by Re = 30, which identifies the practical range of the iteration rather than a proved convergence boundary. We also show what goes wrong when the projection is omitted, as it was in an earlier iteration of the author's: the iterates cease to be divergence-free and an apparent growth appears that belongs to the expansion and not to the flow. For an n-dimensional generalisation of the initial field the fraction of the convective field not absorbed by pressure is exactly 2*sqrt(2)/3 in every dimension n >= 3, and the longitudinal fraction exactly 1/3. The divergence of each returned source is a sharp diagnostic, failing by sixteen orders of magnitude at the step where the projection is omitted; the cell kinetic energy is a weaker one, detecting gross failure only.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22372",
  "author_total": 1,
  "authors": [
    {
      "name": "R. K. Michael Thambynayagam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6s9tpm3hmjrt5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22372",
  "fulltext_url": null,
  "id": "6s9tpm3hmjrt5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22372",
  "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": "W7214033631",
  "pdf_url": "https://arxiv.org/pdf/2609.22372",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6s9tpm3hmjrt5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2609.22372",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22372"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Iterative Construction of n-Dimensional Navier-Stokes Solutions with Non-Gradient Convection",
  "title_text": "Iterative Construction of n-Dimensional Navier-Stokes Solutions with Non-Gradient Convection",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/6s9tpm3hmjrt5",
  "venue": "arXiv",
  "versions": []
}