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


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