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.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.Journal
Kinetic and Related ModelsISSN
1937-5093Handle URI
http://hdl.handle.net/10754/597741ae974a485f413a2113503eed53cd6c53
10.3934/krm.2011.4.277