Celebrating Cercignani's conjecture for the Boltzmann equation - Institut Camille Jordan Accéder directement au contenu
Article Dans Une Revue Kinetic and Related Models Année : 2011

Celebrating Cercignani's conjecture for the Boltzmann equation

Résumé

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.
Fichier principal
Vignette du fichier
pocc18.pdf (265.84 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00519608 , version 1 (20-09-2010)
hal-00519608 , version 2 (12-10-2010)

Identifiants

Citer

Laurent Desvillettes, Clément Mouhot, Cédric Villani. Celebrating Cercignani's conjecture for the Boltzmann equation. Kinetic and Related Models , 2011, 4 (1), pp.277-294. ⟨10.3934/krm.2011.4.277⟩. ⟨hal-00519608v2⟩
473 Consultations
561 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More