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

被引：5

作者：

Ayi, Nathalie ^{[1
]}

Herda, Maxime ^{[2
]}

Hivert, Helene ^{[3
]}

Tristani, Isabelle ^{[4
]}

机构：

[1] Univ Paris, Sorbonne Univ, CNRS, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75005 Paris, France

[2] Univ Lille, INRIA, CNRS, UMR 8524,Lab Paul Painleve, F-59000 Lille, France

[3] Univ Lyon, Ecole Cent Lyon, CNRS, UMR 5208,Inst Camille Jordan, F-69134 Ecully, France

[4] PSL Res Univ, CNRS, Ecole Normale Super, DMA, 45 Rue Ulm, F-75005 Paris, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2020年 / 358卷 / 03期

基金：

欧洲研究理事会;

关键词：

ENTROPIES;

D O I：

10.5802/crmath.46

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Levy-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 Levy-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.

引用

页码：333 / 340

页数：8

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