How to construct explicit decay rates for kinetic Fokker–Planck equations?
Brigati G, Stoltz G. 2025. How to construct explicit decay rates for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis. 57(4), 3587–3622.
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Journal Article
| Published
| English
Scopus indexed
Author
Brigati, GiovanniISTA;
Stoltz, Gabriel
Corresponding author has ISTA affiliation
Department
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, subexponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions–Poincaré inequality and an averaging lemma.
Publishing Year
Date Published
2025-08-01
Journal Title
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial and Applied Mathematics
Acknowledgement
The first author was funded by the European Union's Horizon 2020 research andinnovation program under the Marie Sklodowska-Curie grant agreements 754362 and 101034413,and partially by Project EFI (ANR-17-CE40-0030) of the French National Research Agency (ANR).The work of the second author was partially funded by the European Research Council (ERC) underthe European Union's Horizon 2020 research and innovation programme (grant agreement 810367),and by the Agence Nationale de la Recherche under grants ANR-19-CE40-0010 (QuAMProcs) andANR-21-CE40-0006 (SINEQ).
Volume
57
Issue
4
Page
3587-3622
ISSN
eISSN
IST-REx-ID
Cite this
Brigati G, Stoltz G. How to construct explicit decay rates for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis. 2025;57(4):3587-3622. doi:10.1137/24M1700351
Brigati, G., & Stoltz, G. (2025). How to construct explicit decay rates for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/24M1700351
Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay Rates for Kinetic Fokker–Planck Equations?” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2025. https://doi.org/10.1137/24M1700351.
G. Brigati and G. Stoltz, “How to construct explicit decay rates for kinetic Fokker–Planck equations?,” SIAM Journal on Mathematical Analysis, vol. 57, no. 4. Society for Industrial and Applied Mathematics, pp. 3587–3622, 2025.
Brigati G, Stoltz G. 2025. How to construct explicit decay rates for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis. 57(4), 3587–3622.
Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay Rates for Kinetic Fokker–Planck Equations?” SIAM Journal on Mathematical Analysis, vol. 57, no. 4, Society for Industrial and Applied Mathematics, 2025, pp. 3587–622, doi:10.1137/24M1700351.
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