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

Carrapatoso, Kleber

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

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http://hal.archives-ouvertes.fr/hal-00851757

Date

2015

Nom de la revue

Bulletin des sciences mathématiques

Volume

139

Numéro

Éditeur

Elsevier

Pages

777-805

Résumé (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.

Mots-clés

hard potentials; hypodissipativity; exponential decay; spectral gap; Landau equation