A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium
Analysis of PDEs
2020-03-17 v2
Abstract
In this paper we are interested in the large time behavior of linear kinetic equations with heavy-tailed local equilibria. Our main contribution concerns the kinetic L\'evy-Fokker-Planck equation, for which we adapt hypocoercivity techniques in order to show that solutions converge exponentially fast to the global equilibrium. Compared to the classical kinetic Fokker-Planck equation, the issues here concern the lack of symmetry of the non-local L\'evy-Fokker-Planck operator and the understanding of its regularization properties. As a complementary related result, we also treat the case of the heavy-tailed BGK equation.
Keywords
Cite
@article{arxiv.1911.11535,
title = {A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium},
author = {Nathalie Ayi and Maxime Herda and Hélène Hivert and Isabelle Tristani},
journal= {arXiv preprint arXiv:1911.11535},
year = {2020}
}