Date
2004
Description
47 pages
Lien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00087274/en/
Indexation documentaire
Probabilités et mathématiques appliquées
Subject
Boltzmann equation ; spatially homogeneous ; hard spheres ; hard potentials ; angular cutoff ; regularity theory ; quantitative ; relaxation to equilibrium
Nom de la revue
Archive for Rational Mechanics and Analysis
Volume
173
Numéro
2
Date de publication
08-2004
Pages article
169-212
Nom de l'éditeur
Springer-Verlag
Auteur
Mouhot, Clément
Villani, Cédric
Type
Article accepté pour publication ou publié
Résumé en anglais
We develop the regularity theory of the spatially homogeneous Boltzmann equation with cut-off and hard potentials (for instance, hard spheres), by (i) revisiting the Lp-theory to obtain constructive bounds, (ii) establishing propagation of smoothness and singularities, (iii) obtaining estimates about the decay of the sin- gularities of the initial datum. Our proofs are based on a detailed study of the “regularity of the gain operator”. An application to the long-time behavior is presented.
