{
  "abstract": "We prove that solution maps of the Vlasov--Poisson equation are discontinuous at the zero initial datum in $X_p=L_x^pL_v^\\infty$ for every $1\\leq p<\\infty$, in $\\mathbb{R}^{d} \\times \\mathbb{R}^{d}$ with $d \\le 3$, and for both attractive and repulsive interactions. For every $T>0$, the trajectory of the solution in $L^\\infty([0,T];X_p)$ is discontinuous at zero, and for every sufficiently small fixed $t>0$, the fixed-time map with values in $X_p$ is also discontinuous at zero. The counterexamples are smooth, nonnegative, bounded by one, and supported in a common compact subset of phase space. Their mass and initial $X_p$ norm tend to zero, whereas their solution norm at the observation time is at least one. The construction places narrow spatial packets on a lattice. Free transport allows a different velocity to select a packet at each spatial point, while a smallness estimate on the field ensures that the nonlinear characteristics are close to that of the free transport. For the same families, the phase-space $L^q$ norms converge to zero uniformly in time for every $1\\leq q<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20682",
  "author_total": 4,
  "authors": [
    {
      "name": "Ke Chen"
    },
    {
      "name": "In-Jee Jeong"
    },
    {
      "name": "Quoc-Hung Nguyen"
    },
    {
      "name": "Sangwook Tae"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fb18a4jjbh4vx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20682",
  "fulltext_url": null,
  "id": "fb18a4jjbh4vx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20682",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7213576807",
  "pdf_url": "https://arxiv.org/pdf/2609.20682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fb18a4jjbh4vx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20682"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Discontinuity of the Vlasov--Poisson Flow in $L_x^pL_v^\\infty$",
  "title_text": "Discontinuity of the Vlasov--Poisson Flow in L_x^pL_v^∞",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/fb18a4jjbh4vx",
  "venue": "arXiv",
  "versions": []
}