Year: 2019
Type: preprint
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 Lévy-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 Lévy-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.
Source: arXiv (Cornell University)
Institutions: Centre National de la Recherche Scientifique, Sorbonne Université, Laboratoire Jacques-Louis Lions, Institut national de recherche en sciences et technologies du numérique, Université de Lille, Laboratoire Paul Painlevé, RAPSODI: Approximations numériques fiables pour les systèmes dissipatifs, École Centrale de Lyon, Université de Lyon, Institut Camille Jordan, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département de mathématiques et applications
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4288018098