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Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range

  • Zikai Chen
  • Chongyang Ren
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Abstract

We investigate kinetic Fokker--Planck equations with rough divergence-free drifts in anisotropic mixed Lebesgue spaces. The divergence-free structure yields an energy cancellation that remains effective under kinetic localization. Combining this cancellation with anisotropic regularization estimates and a De Giorgi iteration, we establish local boundedness for weak subsolutions and, consequently, global well-posedness for the Cauchy problem in a scaling-supercritical regime.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026kinetic,
  title = {{Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range}},
  author = {Zikai Chen and Chongyang Ren},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02385},
  eprint = {2609.02385},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02385},
}
RIS
TY  - UNPB
TI  - Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range
AU  - Zikai Chen
AU  - Chongyang Ren
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02385
UR  - https://arxiv.org/abs/2609.02385
AB  - We investigate kinetic Fokker--Planck equations with rough divergence-free drifts in anisotropic mixed Lebesgue spaces. The divergence-free structure yields an energy cancellation that remains effective under kinetic localization. Combining this cancellation with anisotropic regularization estimates and a De Giorgi iteration, we establish local boundedness for weak subsolutions and, consequently, global well-posedness for the Cauchy problem in a scaling-supercritical regime.
ER  -