{
  "abstract": "We prove local Hadamard well-posedness for the three-dimensional incompressible free-boundary ideal magnetohydrodynamic equations without surface tension under the Taylor sign condition. For every $5/2<s<4$, the result holds on bounded fluid domains whose closures are diffeomorphic to the closed ball, with the velocity, magnetic field, and boundary in the standard $H^s$ spaces. No additional regularity in the magnetic direction is required. The proof rests on a fourth order geometric energy inequality whose coefficients are controlled by these $H^s$ norms, the fixed geometric bounds, and the Taylor lower bound. A harmonic extension of the boundary normal provides the coefficient control needed at this regularity. We also prove that, near every admissible initial state and at each positive time in a common local existence interval, the Eulerian solution map is not uniformly continuous on any nonempty open subset of a sufficiently small data neighborhood. The construction combines localized magnetic oscillations prescribed at the observation time with time reversal and Galilean translations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26268",
  "author_total": 2,
  "authors": [
    {
      "name": "Chengchun Hao"
    },
    {
      "name": "Siqi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15jgh6dbvd0em.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26268",
  "fulltext_url": null,
  "id": "15jgh6dbvd0em",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26268",
  "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": "W7223060948",
  "pdf_url": "https://arxiv.org/pdf/2610.26268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15jgh6dbvd0em.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hadamard well-posedness and nonuniform dependence for the incompressible free-boundary ideal MHD equations",
  "title_text": "Hadamard well-posedness and nonuniform dependence for the incompressible free-boundary ideal MHD equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/15jgh6dbvd0em",
  "venue": "arXiv",
  "versions": []
}