{
  "abstract": "We prove that exact quadratic energy cancellation alone does not force growth of the spatial analyticity radius. On $\\mathbb{T}^3$, we construct an explicit symmetric, translation-invariant, first-order bilinear operator $Q$ that preserves the divergence-free class and, for every smooth real-valued divergence-free vector field $v$, satisfies $ \\int_{\\mathbb{T}^3} Q(v,v)\\cdot v\\,dx=0.$ For every prescribed sufficiently small time $T>0$, the equation $\\partial_t u-Δu=Q(u,u)$ admits a global smooth, real-valued, mean-zero, divergence-free solution $u$ such that $\\operatorname{rad}(u(0))=\\operatorname{rad}(u(T))=1$. The construction reduces the dynamics on an invariant cyclic-shear class to viscous Burgers and tunes a Cole-Hopf heat profile so that its nearest complex zero returns to its initial distance from the real torus. For every $1<α<2$ and every prescribed sufficiently small $T>0$, we also construct a symmetric sparse frequency set, its associated Fourier projection, and trigonometric-polynomial initial data for the projected dissipative surface quasi-geostrophic equation. The resulting unique global smooth solution $θ$ has infinite analyticity radius initially but satisfies $0<\\operatorname{rad}(θ(T))\\leq1$. An additively separated Fourier cascade yields coefficientwise exponential lower bounds, while uniform comparison estimates control the feedback interactions. Thus entire analyticity need not persist even from trigonometric-polynomial data. Together, the two constructions show that an exact energy identity alone does not determine the frequency geometry governing analyticity-radius growth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05023",
  "author_total": 4,
  "authors": [
    {
      "name": "Ke Chen"
    },
    {
      "name": "Haina Li"
    },
    {
      "name": "Quoc-Hung Nguyen"
    },
    {
      "name": "Ping Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezc217wy7py7c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05023",
  "fulltext_url": null,
  "id": "ezc217wy7py7c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05023",
  "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",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7211871276",
  "pdf_url": "https://arxiv.org/pdf/2609.05023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezc217wy7py7c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of analyticity-radius growth in energy-canceling fluid models",
  "title_text": "Failure of analyticity-radius growth in energy-canceling fluid models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/ezc217wy7py7c",
  "venue": "arXiv",
  "versions": []
}