{
  "abstract": "This paper is concerned with space inhomogeneous Fermi-Dirac-Fokker-Planck equation posed on a classical kinetic phase space. The nonlinear factor $f(1-f)$ appears both in the transport term and in the collison part of the Fokker-Planck operator, accounting for the exclusion principle of fermions. Solutions are subject to the physical constraint $0\\leq f\\leq 1$. Previous existing results have mainly been obtained under suitable smallness or close-to-equilibrium assumptions. A main difficulty stems from the nonlinear and degenerate parabolic structure of the equation. We prove the existence and uniqueness of global solutions without any smallness or close-to-equilibrium assumptions. To construct solutions, we use a vanishing viscosity approximation by adding a Laplacian in the spatial variable. We derive uniform estimates for the regularized problem and obtain compactness in the space of functions of bounded variation $(BV),$ allowing us to pass to the limit as the spatial viscosity vanishes. Since the limiting equation is degenerate with a nonlinear transport, we formulate an appropriate notion of entropy solutions incorporating the kinetic structure of the equation. We prove uniqueness within this class and show that every vanishing-viscosity limit satisfies the entropy formulation. Our result provides a global well-posedness theory beyond the perturbative regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16700",
  "author_total": 1,
  "authors": [
    {
      "name": "Gayrat Toshpulatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19gmz9ecn8pmh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16700",
  "fulltext_url": null,
  "id": "19gmz9ecn8pmh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16700",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7221811109",
  "pdf_url": "https://arxiv.org/pdf/2610.16700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19gmz9ecn8pmh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16700"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-posedness for the spatially inhomogeneous Fermi-Dirac-Fokker-Planck equation",
  "title_text": "Well-posedness for the spatially inhomogeneous Fermi-Dirac-Fokker-Planck equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/19gmz9ecn8pmh",
  "venue": "arXiv",
  "versions": []
}