{
  "abstract": "We establish Liouville-type theorems for the three-dimensional stationary fractional magnetohydrodynamic (MHD) system with different orders of dissipation. Our first result shows that every smooth solution satisfying the natural homogeneous Sobolev energy conditions is trivial whenever $1\\leqα\\leq 5/3$ and $3\\leqα+2β\\leq5$, without any additional integrability assumptions on the velocity or magnetic fields. This extends previous results to new parameter regimes, including cases with $β<1$. Beyond this region, we prove a complementary Liouville theorem under suitable integrability conditions only on the radial components of the velocity and magnetic fields. The proofs rely on the Caffarelli--Silvestre extension and localized energy estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27494",
  "author_total": 2,
  "authors": [
    {
      "name": "Albert Ai"
    },
    {
      "name": "Gaston Vergara-Hermosilla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7cg9r8jvvxw94.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27494",
  "fulltext_url": null,
  "id": "7cg9r8jvvxw94",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27494",
  "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": "W7223111993",
  "pdf_url": "https://arxiv.org/pdf/2610.27494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7cg9r8jvvxw94.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Liouville Theorems for the Stationary Fractional Magnetohydrodynamic Equations",
  "title_text": "Liouville Theorems for the Stationary Fractional Magnetohydrodynamic Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/7cg9r8jvvxw94",
  "venue": "arXiv",
  "versions": []
}