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Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

Carrapatoso, Kleber (2015), Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials, Bulletin des sciences mathématiques, 139, 7, p. 777-805. 10.1016/j.bulsci.2014.12.002

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00851757
Date
2015
Journal name
Bulletin des sciences mathématiques
Volume
139
Number
7
Publisher
Elsevier
Pages
777-805
Publication identifier
Metadata
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Author(s)
Carrapatoso, Kleber
Abstract (EN)
This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials . We prove an exponential in time convergence towards the equilibrium, improving results of Desvillettes and Villani. Our approach is based on new spectral gap estimates for the linearized Landau operator in weighted (polynomial or stretched exponential) $L^p$-spaces.
Subjects / Keywords
hard potentials; hypodissipativity; exponential decay; spectral gap; Landau equation