{
  "abstract": "In this paper, we study the axisymmetric Hall magnetohydrodynamics where $u = u^re_r+u^ze_z$ and $B = B^θe_θ$. We construct small, smooth, compactly supported, and axisymmetric initial data $(u_{0},B_{0})$ and prove that there is a unique smooth axisymmetric solution with norm inflation in $H^{σ-1}(\\mathbb R^3) \\times H^σ(\\mathbb R^3)$ for $1<σ<7/2$. Moreover, we study the case with fractional dissipation $(-Δ)^βu$ and $(-Δ)^αB$, modifying the initial data slightly and proving that the solution inflates in $H^{σ-1}(\\mathbb R^3) \\times H^σ(\\mathbb R^3)$ for $1<σ<7/2-2\\max\\{α,β\\}$ and $ 0 \\le α, β< 5/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06730",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoming Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kmktw6a0atd1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06730",
  "fulltext_url": null,
  "id": "6kmktw6a0atd1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06730",
  "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": "W7202139068",
  "pdf_url": "https://arxiv.org/pdf/2608.06730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kmktw6a0atd1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.06730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space",
  "title_text": "Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6kmktw6a0atd1",
  "venue": "arXiv",
  "versions": []
}