Celebrating Cercignani's conjecture for the Boltzmann equation

Cédric Villani, Clément Mouhot, Laurent Desvillettes

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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. © American Institute of Mathematical Sciences.
Original languageEnglish (US)
Pages (from-to)277-294
Number of pages18
JournalKinetic and Related Models
Issue number1
StatePublished - Jan 26 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: The authors wish to thank the ANR grant CBDif for support. The second author wishes to thank the Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST) for the funding provided for his repeated visits at Cambridge University during the autumn 2009 and the spring 2010.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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