{
  "abstract": "We consider the Cauchy problem for the one-dimensional full compressible Navier--Stokes equations with general constitutive laws $p=p(v,θ)$ and $e=e(v,θ)$. The pressure and internal energy are assumed to be sufficiently smooth, thermodynamically compatible in the sense that $e_v=θp_θ-p$, and to satisfy $e_θ>0$. We first establish the local-in-time existence and uniqueness of strong solutions for large initial data without imposing monotonicity conditions on the pressure. For perturbations around a constant equilibrium $(\\bar v,0,\\barθ)$, we further assume the mechanical stability condition $p_v(\\bar v,\\barθ)<0$. By introducing a relative thermodynamic energy through the Gibbs relation, we derive a basic energy identity and prove its local quadratic coercivity near the equilibrium. Combining this estimate with higher-order a priori bounds, we obtain the global existence and uniqueness of strong solutions for sufficiently small $H^1(\\mathbb R)$ perturbations. Moreover, the specific volume and temperature remain uniformly bounded away from zero and infinity for all time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15317",
  "author_total": 1,
  "authors": [
    {
      "name": "Qingsong Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nd91jg9avvyy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15317",
  "fulltext_url": null,
  "id": "7nd91jg9avvyy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15317",
  "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": "W7213271887",
  "pdf_url": "https://arxiv.org/pdf/2609.15317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nd91jg9avvyy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Local and Global Existence of Strong Solutions to the One-Dimensional Compressible Navier--Stokes Equations with General Pressure Law",
  "title_text": "Local and Global Existence of Strong Solutions to the One-Dimensional Compressible Navier--Stokes Equations with General Pressure Law",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/7nd91jg9avvyy",
  "venue": "arXiv",
  "versions": []
}