{
  "abstract": "We study the Cauchy problem for the three-dimensional isentropic compressible ideal (inviscid and non-resistive) magnetohydrodynamic equations with velocity damping on the periodic torus $\\mathbb{T}^3$. The system admits a steady equilibrium consisting of a constant density $\\barρ$ and a uniform background magnetic field $ω\\in\\mathbb{R}^3$. We prove that this equilibrium is nonlinearly stable. More precisely, we show that if the initial data are a sufficiently small perturbation of $(\\barρ,\\mathbf{0},ω)$ in the Sobolev space $H^N(\\mathbb{T}^3)$ with $N\\geq 6r+4$, and if $ω$ satisfies a Diophantine condition, then the system admits a unique global smooth solution. Moreover, the perturbations decay algebraically in time. To the best of our knowledge, this is the first global well-posedness result for the multi-dimensional isentropic compressible ideal MHD system. The proof reveals a hidden dissipation mechanism: although neither the density equation nor the magnetic field equation contains explicit diffusion or damping, the coupling between the velocity and the magnetic field through the background field $ω$, combined with a Diophantine--Poincaré inequality, generates effective dissipation for both the density perturbation and the magnetic field perturbation, which together with the velocity damping yields global regularity and time decay.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04462",
  "author_total": 4,
  "authors": [
    {
      "name": "Liening Qiao"
    },
    {
      "name": "Jiahong Wu"
    },
    {
      "name": "Fuyi Xu"
    },
    {
      "name": "Xiaoping Zhai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/594cda17hsa9d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04462",
  "fulltext_url": null,
  "id": "594cda17hsa9d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04462",
  "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": "W7160514252",
  "pdf_url": "https://arxiv.org/pdf/2605.04462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/594cda17hsa9d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2605.04462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04462"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stabilization by a background magnetic field: global well-posedness of the compressible isentropic ideal MHD equations with velocity damping",
  "title_text": "Stabilization by a background magnetic field: global well-posedness of the compressible isentropic ideal MHD equations with velocity damping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/594cda17hsa9d",
  "venue": "arXiv",
  "versions": []
}