{
  "abstract": "We construct piecewise smooth solutions of the full compressible Euler equations that evolve from entropy waves into vortex sheets while retaining a strictly positive Taylor jump. For every integer $κ\\geq1$, we obtain solutions satisfying initial material compatibility for pressure and velocity through order $κ$, whose tangential velocity jump has a nonzero leading term of order $t^{κ+1}$. These solutions are periodic in the tangential variables and admit a smooth realization in a slab with impermeable walls. We also construct solutions on a local nonperiodic tangential patch that satisfy initial material compatibility at every order, yet have a tangential velocity jump that is nonzero for every sufficiently small positive time and flat at $t=0$. The finite-order construction uses a normal Cauchy-Kowalevski problem for velocity potentials, whereas the all-order construction uses a homogeneous reduction to a smooth hyperbolic Cauchy problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32893",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuri Trakhinin"
    },
    {
      "name": "Wei Wang"
    },
    {
      "name": "Zhifei Zhang"
    },
    {
      "name": "Wenbin Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dsk380ngatn70.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32893",
  "fulltext_url": null,
  "id": "dsk380ngatn70",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32893",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7223660319",
  "pdf_url": "https://arxiv.org/pdf/2610.32893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dsk380ngatn70.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "From entropy waves to vortex sheets for the Euler equations",
  "title_text": "From entropy waves to vortex sheets for the Euler equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/dsk380ngatn70",
  "venue": "arXiv",
  "versions": []
}