{
  "abstract": "We extend the global existence results for critical parameters of [Bianchini and Leccese, J. Math. Anal. Appl. (2024)] to the multidimensional problem \\begin{equation*} \\partial_t u + \\text{div } (b(t,x) u^{1+k}) = Δu \\end{equation*} for $b:(0,\\infty)\\times\\mathbb{R}^d\\to\\mathbb{R}^d$ non-autonomous fields, in the case \\begin{equation*} b\\in L^\\infty_{\\mathrm{loc}} \\bigl((0,\\infty),L^{p,\\infty}(\\mathbb{R}^d)\\bigr), \\qquad p>d\\ge 2. \\end{equation*} For the critical case, we study the difference between two ordered solutions whose conserved small mass absorbs the drift. Finitely many increments then reach an arbitrary solution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25764",
  "author_total": 1,
  "authors": [
    {
      "name": "Giacomo Maria Leccese"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bhzh89kjk8neb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25764",
  "fulltext_url": null,
  "id": "bhzh89kjk8neb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25764",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214119400",
  "pdf_url": "https://arxiv.org/pdf/2609.25764",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bhzh89kjk8neb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25764",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25764"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence and Blow-Up for Non-linear Fokker-Planck with Controlled Drift",
  "title_text": "Existence and Blow-Up for Non-linear Fokker-Planck with Controlled Drift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/bhzh89kjk8neb",
  "venue": "arXiv",
  "versions": []
}