Year: 2026
Type: preprint
Abstract: We study the long-time behaviour of solutions to kinetic Fokker-Planck equations with power law confinement potentials and local equilibria with fat tails. Without relying on \emph{a priori} moment bounds or perturbative regimes, we establish global estimates on weighted norms (main result) using two methods: a coupling of the weighted norms with entropy dissipation (DMS method) and a Foster-Lyapunov condition approach. As a consequence, we establish an entropy - entropy production inequality and the convergence rates to equilibrium in terms of the exponents associated to the growth of the spatial confinement and the tail decay of local equilibria. For sake of simplicity, we assume that stationary states are factorized.
Source: arXiv (Cornell University)
Authors: Bouin, Émeric, Dolbeault, Jean, Ziviani, Luca
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204855454