{
  "abstract": "We study the long-time pointwise behavior of small localized perturbations of a constant state for the one-dimensional compressible isentropic Navier-Stokes equations. After subtracting the two Burgers diffusion waves, the convergent sum of all higher-order diffusion waves, and the cross-family viscous corrections, we prove a cone-preserving pointwise estimate for the exact physical remainder and, in particular, \\[ |R_i(x,t)|\\leq C E_N\\log(2+t)Ψ_i(x,t), \\qquad \\sup_{x\\in\\mathbb R}Ψ_i(x,t)\\leq C(1+t)^{-1}. \\] Here \\(E_N\\) measures the size of the initial data and \\(Ψ_i\\) is the cone-resolved weight; both are defined precisely in the main theorem below. Thus $\\|R_i(t)\\|_{L^\\infty}\\leq C E_N(1+t)^{-1}\\log(2+t)$. The key new idea is to apply a familywise Cole--Hopf transformation to the spatial antiderivative of the remainder, which exactly eliminates the critical same-family first-order feedback. We further construct an approximate Green function adapted to the two characteristic families and combine it with Gaussian-mode extraction and a Kawashima-type energy argument. This yields a cone-preserving estimate at the limiting decay rate, up to a logarithmic loss.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11707",
  "author_total": 4,
  "authors": [
    {
      "name": "Rui Li"
    },
    {
      "name": "Xu Song"
    },
    {
      "name": "Guanghui Wang"
    },
    {
      "name": "Lingda Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bhdgvpdw10gv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11707",
  "fulltext_url": null,
  "id": "1bhdgvpdw10gv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11707",
  "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": "W7212303698",
  "pdf_url": "https://arxiv.org/pdf/2609.11707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bhdgvpdw10gv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Limiting Pointwise Decay for the compressible isentropic Navier-Stokes equations",
  "title_text": "Limiting Pointwise Decay for the compressible isentropic Navier-Stokes equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/1bhdgvpdw10gv",
  "venue": "arXiv",
  "versions": []
}