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arXiv · 1911.11535

A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium

Nathalie Ayi·Maxime Herda·Hélène Hivert·Isabelle Tristani
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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.

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Nathalie Ayi, Maxime Herda, Hélène Hivert, Isabelle Tristani. 2019-11-26. A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium. https://arxiv.org/abs/1911.11535

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