Date
2011
Lien vers un document non conservé dans cette base
http://arxiv.org/abs/1009.4006v2
Indexation documentaire
Analyse
Subject
Cercignani's conjecture; spectral gap; Boltzmann equation; relative entropy; entropy production; relaxation to equilibrium; Landau equation; logarithmic Sobolev inequality; Poincaré inequality
Nom de la revue
Kinetic and related models
Volume
4
Numéro
1
Date de publication
2011
Pages article
277-294
Nom de l'éditeur
American Institute of Mathematical Sciences
Auteur
Desvillettes, Laurent
Mouhot, Clément
Villani, Cédric
Type
Article accepté pour publication ou publié
Résumé en anglais
Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.
