{
  "abstract": "We consider the limit $δ\\to1^+$ for the one-dimensional compressible Navier-Stokes equations with viscosity $μ(ρ)=ρ^δ$ and far field vacuum. To the best of our knowledge, this is the first result on the viscosity-exponent limit $δ\\to1^+$ for strong solutions with far field vacuum. With far field vacuum, the diffusion coefficient $ρ^{δ-1}$ does not converge uniformly to $1$ on $\\mathbb R$ as $δ\\to1^+$. The main difficulty is to obtain uniform estimates for this limit. By introducing some new weighted density variables, we establish local well-posedness and uniform estimates without requiring $ρ_0^{(δ-1)/2}\\in L^2(\\mathbb R)$. We prove strong convergence to the known global $δ=1$ solution obtained in \\cite{WenZhangDCDS2025} on a local time interval independent of $δ$. With one additional order of regularity of the initial data and the limit solution, the convergence holds on every fixed finite time interval, and the maximal life-spans of the $δ>1$ solutions tend to $+\\infty$ as $δ\\to1^+$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07790",
  "author_total": 1,
  "authors": [
    {
      "name": "Xingyang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vfcbhjm3zqm1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07790",
  "fulltext_url": null,
  "id": "9vfcbhjm3zqm1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07790",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07790",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vfcbhjm3zqm1.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07790"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Singular viscosity-exponent limit for one-dimensional compressible Navier-Stokes equations with far field vacuum",
  "title_text": "Singular viscosity-exponent limit for one-dimensional compressible Navier-Stokes equations with far field vacuum",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/9vfcbhjm3zqm1",
  "venue": "arXiv",
  "versions": []
}