Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 13 min ago
PreprintarXiv licencearXiv

Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups

  • Jean-François Jabir
  • Damir Kinzebulatov
  • Chengjun Yue
Open at sourcePDFDOICite

Abstract

We develop a Sobolev theory for the kinetic Fokker-Planck equation subject to a singular Morrey-form L∞+MqK 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.

Related

  1. Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range
    Zikai Chen, Chongyang Ren
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Weighted L2 bounds for kinetic Fokker-Planck equations and hypocoercivity
    Émeric Bouin, Jean Dolbeault, Luca Ziviani
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv
  3. Hypocoercivity-preserving space-time Galerkin methods for kinetic Fokker-Planck equations
    Zhaonan Dong, Emmanuil H Georgoulis
    HALPreprintCC BY 4.0Full textNumerical analysis & scientific computingHALarXiv
  4. On uniqueness of probability solutions to one-dimensional Fokker-Planck-Kolmogorov equations
    Vladimir I. Bogachev, Stanislav V. Shaposhnikov
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsProbabilityarXiv
  5. Fundamental solutions to Kolmogorov-Fokker-Planck equations with unbounded lower order terms
    Pascal Auscher
    HALPreprintCC BY-NC 4.0Full textAnalysis & PDEsHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{jabir2026kinetic,
  title = {{Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups}},
  author = {Jean-François Jabir and Damir Kinzebulatov and Chengjun Yue},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17319},
  eprint = {2610.17319},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17319},
}
RIS
TY  - UNPB
TI  - Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups
AU  - Jean-François Jabir
AU  - Damir Kinzebulatov
AU  - Chengjun Yue
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17319
UR  - https://arxiv.org/abs/2610.17319
AB  - We develop a Sobolev theory for the kinetic Fokker-Planck equation subject to a singular Morrey-form L^∞+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.
ER  -