How to construct decay rates for kinetic Fokker--Planck equations? - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

How to construct decay rates for kinetic Fokker--Planck equations?

Résumé

We study time averages for the norm of the solution to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide explicit and constructive decay estimates, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The evolution is subject to a transport operator induced by an external space-confining force. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions-Poincaré inequality and an averaging lemma.

Dates et versions

hal-04334470 , version 1 (11-12-2023)

Identifiants

Citer

Giovanni Brigati, Gabriel Stoltz. How to construct decay rates for kinetic Fokker--Planck equations?. 2023. ⟨hal-04334470⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More