{
  "abstract": "We investigate the ill-posedness mechanism of the hard-sphere Boltzmann equation in $H_{x}^{s}$ Sobolev space. Via a direct construction, we prove a strong-weak type ill-posedness result in the low-regularity regime $s<1$, establishing a sharp threshold in connection to the local $s>1$ well-posedness result [11]. Instead of originating from the large-velocity growth of the collision kernel, this illposedness is generated by the loss term and dispersive effects. Consequently, we prove a dispersion-driven nonlinear instability mechanism for the hard-sphere Boltzmann equation, and provide a capstone of the ill-posedness series [18,20].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.01331",
  "author_total": 4,
  "authors": [
    {
      "name": "Xuwen Chen"
    },
    {
      "name": "Yan Guo"
    },
    {
      "name": "Shunlin Shen"
    },
    {
      "name": "Zhifei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7n3s32f4jwse.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.01331",
  "fulltext_url": null,
  "id": "b7n3s32f4jwse",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.01331",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7163259176",
  "pdf_url": "https://arxiv.org/pdf/2606.01331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7n3s32f4jwse.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2606.01331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.01331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation",
  "title_text": "Sharp H_x^s Ill-posedness of the Hard-sphere Boltzmann Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/b7n3s32f4jwse",
  "venue": "arXiv",
  "versions": []
}