{
  "abstract": "We study the inviscid limit of the one-dimensional viscous Burgers equation from smooth initial data through nondegenerate shock formation and subsequent shock development. Chaturvedi and Graham \\cite{CG} obtained sharp estimates of order $ν^{1/4}$ up to the shock-formation time. We extend their analysis beyond this time, comparing the viscous solution with the inviscid entropy solution evolving from the same initial data. With the shock-formation time normalized to $t=0$, we prove a pointwise error bound on a fixed interval $0\\leq t \\leq \\bar{\\varepsilon}$, where $\\bar{\\varepsilon}>0$ is independent of the viscosity $ν$. The bound consists of a term of order $ν^{1/4}$ and an exponentially localized contribution originating from the viscous shock layer. The proof is based on matching an outer expansion, an inner expansion near the formation point, and a viscous shock-profile expansion. Combined with the results of Chaturvedi and Graham, this yields a quantitative description of the inviscid limit from the initial time through the development of the young shock.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16420",
  "author_total": 3,
  "authors": [
    {
      "name": "Chao Wang"
    },
    {
      "name": "Yueyi Yang"
    },
    {
      "name": "Zhifei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7aa6q1pf4vsgt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16420",
  "fulltext_url": null,
  "id": "7aa6q1pf4vsgt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16420",
  "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",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7221827162",
  "pdf_url": "https://arxiv.org/pdf/2610.16420",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7aa6q1pf4vsgt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16420",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16420"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Inviscid Limit of Viscous Burgers through Shock Formation and Development",
  "title_text": "The Inviscid Limit of Viscous Burgers through Shock Formation and Development",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7aa6q1pf4vsgt",
  "venue": "arXiv",
  "versions": []
}