Nonlinear kinetic Fokker-Planck equations: existence and diffusion limits

Emeric Bouin; Jean Dolbeault; Antoine Mellet

Nonlinear kinetic Fokker-Planck equations: existence and diffusion limits

Analysis of PDEs 2026-06-30 v1

Authors: Emeric Bouin , Jean Dolbeault , Antoine Mellet

Abstract

In this paper, we focus on a new type of non-linear kinetic Fokker-Planck equation where the non-linearity comes from a non-linear diffusion in the velocity variable. The existence of solutions in suitable Lebesgue spaces is proved, together with important entropy estimates on these solutions. We then study the diffusive limit of such equation.

Cite

@article{arxiv.2606.31899,
  title  = {Nonlinear kinetic Fokker-Planck equations: existence and diffusion limits},
  author = {Emeric Bouin and Jean Dolbeault and Antoine Mellet},
  journal= {arXiv preprint arXiv:2606.31899},
  year   = {2026}
}