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

Giovanni Brigati; Gabriel Stoltz

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arXiv · 2302.14506

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

Giovanni Brigati·Gabriel Stoltz

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Abstract

We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The key step in our estimates is a modified Poincar\'e inequality, obtained via a Lions--Poincar\'e inequality and an averaging lemma.

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Giovanni Brigati, Gabriel Stoltz. 2023-02-28. How to construct decay rates for kinetic Fokker--Planck equations?. https://arxiv.org/abs/2302.14506

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