{
  "abstract": "We consider the Cauchy problem on the real line for a one-dimensional transverse-field isentropic non-resistive magnetohydrodynamic system with viscosity $μ(ρ)=αρ^δ$, $0<δ\\leq1$, and vacuum at spatial infinity. The viscosity therefore vanishes precisely where the density vanishes. We establish two global large-data theorems, one for the sublinear range $0<δ<1$ and one for the linear case $δ=1$, in a nontrivial invariant class of magnetic fields. The class is described by the frozen-in flux $h=b/ρ$ and its mass derivative $k=ρ^{-1}h_x$. The key identity $[\\partial_t+u\\partial_x,ρ^{-1}\\partial_x]=0$ transports both $h$ and $k$, removes all negative powers of the density from the Lorentz force, and propagates the magnetic regularity. A modified effective-velocity entropy contains an additional coercive magnetic term, while its only error is controlled by $k$. Magnetic pressure also strengthens the density upper bound. These estimates close the large-data continuation argument in the ranges $0<δ<1$, $γ\\geqδ+\\tfrac12$, and $δ=1$, $γ>\\tfrac32$. As a result, we extend the work of Cao, Li, and Zhu (SIAM J. Math. Anal., 2022) from the Navier-Stokes equations to the MHD equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13248",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhaoyang Shang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bp3xcsmyerxe6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13248",
  "fulltext_url": null,
  "id": "bp3xcsmyerxe6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13248",
  "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": "W7221576919",
  "pdf_url": "https://arxiv.org/pdf/2610.13248",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bp3xcsmyerxe6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13248",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13248"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global Regular Solutions for One-Dimensional Degenerate Compressible Non-Resistive MHD Equations with Large Data and Far-Field Vacuum",
  "title_text": "Global Regular Solutions for One-Dimensional Degenerate Compressible Non-Resistive MHD Equations with Large Data and Far-Field Vacuum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/bp3xcsmyerxe6",
  "venue": "arXiv",
  "versions": []
}