{
  "abstract": "We develop a Sobolev theory for the kinetic Fokker-Planck equation subject to a singular Morrey-form $L^\\infty+M^q_K$ force field which can produce local blow-ups due to strong attraction to a submanifold. Our approach is based on the fractional representation for the Duhamel series of the equation and on establishing kinetic Adams-type estimates. Accordingly, we construct weak solutions of Brownian-driven kinetic SDEs in a critical Morrey set-up, obtain kinetic Krylov-type estimates and a strongly continuous Feller propagator, and establish uniqueness criteria for a large class of weak solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17319",
  "author_total": 3,
  "authors": [
    {
      "name": "Jean-François Jabir"
    },
    {
      "name": "Damir Kinzebulatov"
    },
    {
      "name": "Chengjun Yue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddft7ttavm6sp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17319",
  "fulltext_url": null,
  "id": "ddft7ttavm6sp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17319",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7221806499",
  "pdf_url": "https://arxiv.org/pdf/2610.17319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddft7ttavm6sp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.17319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17319"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups",
  "title_text": "Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/ddft7ttavm6sp",
  "venue": "arXiv",
  "versions": []
}