{
  "abstract": "In this paper, we study the global regularity of the one-dimensional hypo-viscous compressible Navier--Stokes equations in the critical Besov spaces, where the initial data are close to the constant equilibrium state. We introduce an effective velocity, constructed as a combination of the density and the velocity, which is used to capture the high-frequency behavior of $a$. By performing elaborate high-frequency and low-frequency estimates together with a bootstrap argument, we obtain global existence for $\\frac{1}{2}\\leβ<1$. In particular, when $\\frac{1}{2}\\leβ<\\frac{3}{4}$, we also prove the uniqueness of solutions. Furthermore, under an additional low-frequency assumption, we establish the optimal time decay rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25889",
  "author_total": 3,
  "authors": [
    {
      "name": "Chen Liang"
    },
    {
      "name": "Zhaonan Luo"
    },
    {
      "name": "Zhaoyang Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d6dphfm0bw91.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25889",
  "fulltext_url": null,
  "id": "4d6dphfm0bw91",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25889",
  "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",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7223060026",
  "pdf_url": "https://arxiv.org/pdf/2610.25889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d6dphfm0bw91.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces",
  "title_text": "Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4d6dphfm0bw91",
  "venue": "arXiv",
  "versions": []
}