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Preprints, Working Papers, ... Year : 2023

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

Abstract

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 and versions

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

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