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dc.contributor.authorVillani, Cédric
dc.contributor.authorMouhot, Clément
dc.contributor.authorDesvillettes, Laurent
dc.date.accessioned2016-02-25T12:55:53Z
dc.date.available2016-02-25T12:55:53Z
dc.date.issued2011-01-26
dc.identifier.citationVillani C, Mouhot C, Desvillettes L (2011) Celebrating Cercignani’s conjecture for the Boltzmann equation. KRM 4: 277–294. Available: http://dx.doi.org/10.3934/krm.2011.4.277.
dc.identifier.issn1937-5093
dc.identifier.doi10.3934/krm.2011.4.277
dc.identifier.urihttp://hdl.handle.net/10754/597741
dc.description.abstractCercignani'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.
dc.description.sponsorshipThe 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.
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.subjectBoltzmann equation
dc.subjectCercignani's conjecture
dc.subjectEntropy production
dc.subjectLandau equation
dc.subjectLogarithmic sobolev inequality
dc.subjectPoincare inequality.
dc.subjectRelative entropy
dc.subjectRelaxation to equilibrium
dc.subjectSpectral gap
dc.titleCelebrating Cercignani's conjecture for the Boltzmann equation
dc.typeArticle
dc.identifier.journalKinetic and Related Models
dc.contributor.institutionEcole Normale Superieure de Cachan, Cachan, France
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
dc.contributor.institutionUniversite Claude Bernard Lyon 1, Villeurbanne, France
kaust.grant.numberKUK-I1-007-43
dc.date.published-online2011-01-26
dc.date.published-print2011


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