Convergence to a non-explicit steady state in non-factorized kinetic Fokker-Planck equations with (very) weak velocity confinements

2025/10/14 by Bouin, Emeric, Ziviani, Luca · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.12331

Abstract

In this article, we prove some convergence results for kinetic Fokker-Planck equations with strong space confinement but fat-tailed local equilibria and non-explicit global steady states. We extend the results of \citeC21 to a wider class of fat-tailed local equilibria, with rates of convergence in a large class of weighted \sfL¹ spaces. We complement our results with numerical simulations to investigate the shape of the non-explicit steady state.

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Cited by

• Discrete H-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity

Related

• The kinetic Fokker-Planck equation with weak confinement force
• Exponential stability and hypoelliptic regularization for the kinetic Fokker-Planck equation with confining potential
• \mathrm L² Hypocoercivity methods for kinetic Fokker-Planck equations with factorised Gibbs states
• A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium
• On a class of Fokker-Planck equations with subcritical confinement