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Celebrating Cercignani's conjecture for the Boltzmann equation

Desvillettes, Laurent; Mouhot, Clément; Villani, Cédric (2011), Celebrating Cercignani's conjecture for the Boltzmann equation, Kinetic and related models, 4, 1, p. 277-294. http://dx.doi.org/10.3934/krm.2011.4.277

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1009.4006v2
Date
2011
Journal name
Kinetic and related models
Volume
4
Number
1
Publisher
American Institute of Mathematical Sciences
Pages
277-294
Publication identifier
http://dx.doi.org/10.3934/krm.2011.4.277
Metadata
Show full item record
Author(s)
Desvillettes, Laurent
Mouhot, Clément
Villani, Cédric
Abstract (EN)
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.
Subjects / Keywords
Cercignani's conjecture; spectral gap; Boltzmann equation; relative entropy; entropy production; relaxation to equilibrium; Landau equation; logarithmic Sobolev inequality; Poincaré inequality

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