Conditional hypocoercivity for nonlinear kinetic Fokker--Planck equations
arXiv:2607.26616
summary
The paper studies how solutions of nonlinear kinetic Fokker–Planck equations with porous‑medium diffusion approach equilibrium over time, proving exponential convergence in L¹ under certain macroscopic bounds.
Abstract
We investigate the long-time behaviour of nonlinear kinetic Fokker--Planck equations with porous medium diffusion in a non-perturbative setting. Under a priori conditional bounds on macroscopic quantities, we establish exponential convergence to equilibrium in . These bounds are automatically satisfied if the initial data is trapped between two global equilibrium profiles. Our approach combines the entropy-entropy dissipation structure and some techniques from -hypocoercivity.
14 pages
Topics & keywords
#kinetic equations#fokker‑planck#hypocoercivity#long-time behavior#entropy methods#porous‑medium diffusionnonlinear kinetic Fokker–Planckhypocoercivityentropy dissipationexponential convergenceL¹ convergenceporous medium diffusion