{
  "abstract": "In a smoothly bounded domain $\\Om\\subset\\R^n$ with $n\\geq 1$ and $a>0$, we consider an initial-boundary value problem for the general viscous wave equation \\bas h(u,u_t) u_{tt} = \\Del u_t + a\\Del u + f(u,u_t,\\na u,\\na u_t) \\eas which appears in models of nonlinear acoustics wave propagation; well-established equations of Kuznetsov and Westervelt type form particular examples.\\abs % While the existing literature offers extensive results on global solutions for sufficiently small initial data $(u_{0}, u_{0t})=(u, u_{t})|_{t=0}$ in second- and higher-order Sobolev spaces it appears to remain open how far global solvability can be established under smallness conditions involving only first-order Sobolev spaces. The present manuscript addresses this question by proving the existence of global classical solutions together with exponential decay of the pair $(u,u_{t})$ in $ W^{1,r}\\times W^{1,p}$-Sobolev spaces whenever the nonlinearities $h$ and $f$ are sufficiently smooth and are such that $h(0,0)>0$ as well as $f(0,0,0,0)=0$ and $\\na f(0,0,0,0)=0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02795",
  "author_total": 2,
  "authors": [
    {
      "name": "Tahir Boudjeriou"
    },
    {
      "name": "Michael Winkler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nx6r9a2wknpj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02795",
  "fulltext_url": null,
  "id": "9nx6r9a2wknpj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02795",
  "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",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7207735035",
  "pdf_url": "https://arxiv.org/pdf/2609.02795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nx6r9a2wknpj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global smooth behavior in Kuznetsov and Westervelt type viscous wave equations: A unifying approach covering $W^{1,q}$-small initial data",
  "title_text": "Global smooth behavior in Kuznetsov and Westervelt type viscous wave equations: A unifying approach covering W^1,q-small initial data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/9nx6r9a2wknpj",
  "venue": "arXiv",
  "versions": []
}