{
  "abstract": "We study viscous, non-resistive magnetohydrodynamics on $\\mathbb R^d$, $d\\in\\{2,3\\}$. For every fixed magnetic exponent $s>d/2$ and every velocity exponent $q<s-1$, we prove norm inflation at the origin in $H^q\\times H^s$. Arbitrarily small divergence-free Schwartz data generate classical solutions whose magnetic $H^s$ norm becomes arbitrarily large at arbitrarily small positive times, while the velocity remains arbitrarily small in $H^q$ throughout the observation interval. Together with endpoint local well-posedness, this identifies $q=s-1$ as the sharp lower velocity threshold for fixed $s>d/2$. The construction uses a symmetric pair of high-frequency velocity packets and a fixed low-frequency magnetic profile. A Fourier component of their stretching interaction has a fixed sign and gains the power $K^{s-1-q}$ on a short diffusive time scale. Subtracting an exact reference flow and using endpoint Besov estimates controls the full nonlinear remainder. Quantitative higher-order estimates ensure existence through the observation time and yield the uniform smallness of the velocity in the target norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01124",
  "author_total": 1,
  "authors": [
    {
      "name": "Yinghui Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6d30yh3vs5b7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01124",
  "fulltext_url": null,
  "id": "d6d30yh3vs5b7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01124",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6d30yh3vs5b7.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Magnetic norm inflation below the velocity regularity threshold for viscous non-resistive MHD",
  "title_text": "Magnetic norm inflation below the velocity regularity threshold for viscous non-resistive MHD",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/d6d30yh3vs5b7",
  "venue": "arXiv",
  "versions": []
}