{
  "abstract": "We establish local existence and uniqueness of solutions for the ideal incompressible magnetohydrodynamics system posed on $[0,T]\\times\\mathbb{R}^n$, $n\\ge2$, with a nonzero constant initial magnetic field $\\mathbf{B}_0$ and arbitrary divergence-free velocity data $v_0\\in H^s$, in the range $(n+1)/2<s\\le n/2+1$. The proof uses a Lagrangian wave--Hodge reformulation and exploits an Alfvén null--structure hidden in the pressure forcing. In particular, the constructed Eulerian solutions are induced by a bi-Lipschitz measure-preserving flow map. Zhang first identified this null-structure in \\cite{Zhang2024}; the present work provides a self-contained bridge from that Lagrangian theory to the Eulerian Cauchy problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01093",
  "author_total": 1,
  "authors": [
    {
      "name": "Matteo Giardi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exy7jfpvzp4xp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01093",
  "fulltext_url": null,
  "id": "exy7jfpvzp4xp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01093",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7206203099",
  "pdf_url": "https://arxiv.org/pdf/2609.01093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exy7jfpvzp4xp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Ideal MHD below the classical well-posedness threshold",
  "title_text": "Ideal MHD below the classical well-posedness threshold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/exy7jfpvzp4xp",
  "venue": "arXiv",
  "versions": []
}