{
  "abstract": "We study the two-dimensional periodic resistive compressible magnetohydrodynamic equations with constant shear viscosity and magnetic diffusivity, bulk viscosity $ρ^β$, and pressure $ρ^γ$. For every $β>1$ and $γ>1$, we construct global finite-energy renormalized weak solutions from strictly positive bounded $W^{1,q}$ densities, $q>2$, and arbitrary $H^1$ velocity and magnetic data. The construction combines approximation-independent finite density moments, generalized effective-flux identities, and a joint logarithmic renormalization of the density and its entropy defect. An augmented relative energy containing the $β$-power density potential yields weak--strong uniqueness against positive $H^2$ strong solutions for the same full pressure range. We also establish global strong existence for a large-background family when $γ>\\max\\{5-2β,β+1\\}$. Writing $m=\\intρ_0$, the density perturbation is bounded in the scaled norm $m^{(γ-3)/2}\\|ρ_0-m\\|_{H^2}$, while the fixed $H^2$ velocity and magnetic norms need not be small. For sufficiently large $m$, frequency-dependent acoustic dissipation, staged vorticity weights, and a separate initial-layer flux estimate close a simultaneous bootstrap. The admissible pressure exponents have infimum $7/3$, with the endpoint excluded. For $β>2$ the relevant damping rate is the minimum of the viscous and pressure-relaxation rates; keeping both rates extends the argument without an upper restriction on $β$. The strong theorem has no upper restriction on $γ$ under this scaled density hypothesis; for fixed additive density perturbations it applies in the stated lower range up to $γ=3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05312",
  "author_total": 3,
  "authors": [
    {
      "name": "Yachun Li"
    },
    {
      "name": "Peng Lu"
    },
    {
      "name": "Zhaoyang Shang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dg7aj6tds4s5b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05312",
  "fulltext_url": null,
  "id": "dg7aj6tds4s5b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05312",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7220649367",
  "pdf_url": "https://arxiv.org/pdf/2610.05312",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dg7aj6tds4s5b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05312",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05312"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global solutions to the two-dimensional compressible MHD equations with density-dependent bulk viscosity",
  "title_text": "Global solutions to the two-dimensional compressible MHD equations with density-dependent bulk viscosity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dg7aj6tds4s5b",
  "venue": "arXiv",
  "versions": []
}