{
  "abstract": "We prove non-uniqueness for the forced one-dimensional Vlasov-Poisson equation on the whole space. More precisely, for every finite $p$, we construct a nonnegative ion density, smooth for positive times, and a source $S\\in C([0,1];L^1(\\R^2))$ with $S(0)=0$, for which there exist two distinct nonnegative distributional solutions $f_\\pm\\in C([0,1];L^1(\\R^2))$ with the same zero initial datum and with spatial densities bounded in $L^p(\\R)$ uniformly in time. The result is sharp in terms of the integrability of the spatial densities: our solutions have Lipschitz electric fields, and we show that in this class uniqueness holds as soon as the spatial density is bounded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31629",
  "author_total": 1,
  "authors": [
    {
      "name": "Mikaela Iacobelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9g9a8ejnfbyeg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31629",
  "fulltext_url": null,
  "id": "9g9a8ejnfbyeg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31629",
  "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|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7223332458",
  "pdf_url": "https://arxiv.org/pdf/2610.31629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9g9a8ejnfbyeg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-uniqueness for the forced one-dimensional Vlasov-Poisson equation",
  "title_text": "Non-uniqueness for the forced one-dimensional Vlasov-Poisson equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/9g9a8ejnfbyeg",
  "venue": "arXiv",
  "versions": []
}