{
  "abstract": "We construct global finite-energy weak solutions for a 1D barotropic Navier--Stokes--Maxwell system with displacement current and the algebraic Ohm law. The result holds for every \\(γ>1\\) and arbitrary finite-energy initial data, allowing vacuum and requiring only \\(L^2\\) initial electromagnetic fields. A key ingredient is a weak-to-strong compactness principle for the Maxwell--Ohm subsystem: weak convergence of the velocity coefficients in \\(L^2_tH^1_x\\), together with strong convergence of the initial fields, yields strong electromagnetic trajectories in \\(C_tL^2_x\\). This permits identification of the weak current and the distributional Lorentz force without strong convergence of the velocity. The electromagnetic closure is combined with the classical artificial-viscosity and artificial-pressure construction for compressible flow. A density-primitive effective-flux argument identifies the physical pressure and eliminates the physical and artificial pressure-concentration defects.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24960",
  "author_total": 1,
  "authors": [
    {
      "name": "Cheneg Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/027dh2k28ag1z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24960",
  "fulltext_url": null,
  "id": "027dh2k28ag1z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24960",
  "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": "W7214012100",
  "pdf_url": "https://arxiv.org/pdf/2609.24960",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/027dh2k28ag1z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24960",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24960"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D",
  "title_text": "Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/027dh2k28ag1z",
  "venue": "arXiv",
  "versions": []
}