{
  "abstract": "For a C1 family of smooth closed genus-zero surfaces, we study the quadratic normal jet of unforced surface Navier–Stokes flow near the zero equilibrium. Under an isolated rank-three Riesz slow block and a three-weight slow–fast gap, local C2 invariant graphs share this quotient-valued second derivative after tangent-input identification, without requiring uniqueness of the full graph. A fixed-complement representative is C1 in shape in a bilinear Sobolev-operator norm with infinite-dimensional output. An exact covariance law handles admissible comparisons, including spatial transports with derivative loss. At the unit sphere, the jet vanishes. For symmetric affine deformations, its first variation is a degree-three spherical-harmonic tensor with coefficient −1/(45ν), vanishing exactly for scalar deformation matrices. For each fixed nonscalar D, the jet is therefore nonzero for all sufficiently small 0<|δ|<δ0(D). The onset is local and non-quantitative; no explicit value of δ0(D) is obtained.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Basic Sciences, Common First Year Deanship, King Saud University, Riyadh 12373, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Amr M. Y. Abdelaty",
      "orcid": "0009-0008-6151-5979"
    },
    {
      "affs": [
        0
      ],
      "name": "Hesham A. Abdelghafar"
    },
    {
      "affs": [
        0
      ],
      "name": "Ibrahim S. Elshazly",
      "orcid": "0000-0001-6364-3327"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8xq5cjb4xqas.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214044",
  "fulltext_url": null,
  "id": "b8xq5cjb4xqas",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4044",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/b8xq5cjb4xqas.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T00:20:49Z",
      "native_id": "10.3390/math14214044",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4044"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Shape Differentiation and Anisotropy Onset of Quadratic Invariant-Manifold Jets in Surface Navier–Stokes Flow",
  "title_text": "Shape Differentiation and Anisotropy Onset of Quadratic Invariant-Manifold Jets in Surface Navier–Stokes Flow",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:06Z",
  "url": "https://research.draconitic.com/paper/b8xq5cjb4xqas",
  "venue": "Mathematics",
  "versions": []
}