Celebrating Cercignani's conjecture for the Boltzmann equation

Handle URI:
http://hdl.handle.net/10754/597741
Title:
Celebrating Cercignani's conjecture for the Boltzmann equation
Authors:
Villani, Cédric; Mouhot, Clément; Desvillettes, Laurent
Abstract:
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.
Citation:
Villani 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.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Kinetic and Related Models
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jan-2011
DOI:
10.3934/krm.2011.4.277
Type:
Article
ISSN:
1937-5093
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorVillani, Cédricen
dc.contributor.authorMouhot, Clémenten
dc.contributor.authorDesvillettes, Laurenten
dc.date.accessioned2016-02-25T12:55:53Zen
dc.date.available2016-02-25T12:55:53Zen
dc.date.issued2011-01en
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.en
dc.identifier.issn1937-5093en
dc.identifier.doi10.3934/krm.2011.4.277en
dc.identifier.urihttp://hdl.handle.net/10754/597741en
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.en
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.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectBoltzmann equationen
dc.subjectCercignani's conjectureen
dc.subjectEntropy productionen
dc.subjectLandau equationen
dc.subjectLogarithmic sobolev inequalityen
dc.subjectPoincare inequality.en
dc.subjectRelative entropyen
dc.subjectRelaxation to equilibriumen
dc.subjectSpectral gapen
dc.titleCelebrating Cercignani's conjecture for the Boltzmann equationen
dc.typeArticleen
dc.identifier.journalKinetic and Related Modelsen
dc.contributor.institutionEcole Normale Superieure de Cachan, Cachan, Franceen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionUniversite Claude Bernard Lyon 1, Villeurbanne, Franceen
kaust.grant.numberKUK-I1-007-43en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.