{
  "abstract": "We prove the global well-posedness and nonlinear stability of classical solutions to the three-dimensional compressible viscous, non-resistive MHD system on $\\mathbb{T}^3$ near the equilibrium $(1,\\mathbf{0},\\mathbf{e}_3)$, for small $x_3$-symmetric perturbations and without any Diophantine condition on the background magnetic field. The central obstruction is the $x_3$-independent sector, in which the density and the magnetic field possess no dissipation, no damping, and no decay. We overcome it by exhibiting a hidden wave structure for the exact total pressure $\\mathcal{D}=P(1+a)+B_3+\\frac12|\\mathbf{B}|^2$, the averaged pair $(\\overline{\\mathbf{u}},\\overline{\\mathcal{D}})$ obeys a closed system, and $\\overline{\\mathcal{D}}$ satisfies a strongly damped wave equation whose principal wave part propagates at the fast magnetosonic speed and whose non-parabolic branch damps at a rate that involves no gain of derivatives. This hidden damping substitutes for the missing magnetic dissipation, and simultaneously absorbs the magnetic pressure $\\frac12\\nabla|\\mathbf{B}|^2$, the main obstruction created by compressibility. Together with a damped wave structure for the oscillatory sector and space-time weighted energy functionals with shifted time weights, this yields global existence, uniform stability, and explicit polynomial decay rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14244",
  "author_total": 4,
  "authors": [
    {
      "name": "Lin-An Li"
    },
    {
      "name": "Qian Li"
    },
    {
      "name": "Jiahong Wu"
    },
    {
      "name": "Xiaojing Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dykr49zhntckd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14244",
  "fulltext_url": null,
  "id": "dykr49zhntckd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14244",
  "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": "W7213274894",
  "pdf_url": "https://arxiv.org/pdf/2609.14244",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dykr49zhntckd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14244",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14244"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields",
  "title_text": "Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/dykr49zhntckd",
  "venue": "arXiv",
  "versions": []
}