Celebrating Cercignani's conjecture for the Boltzmann equation
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.
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Cite
@article{arxiv.1009.4006,
title = {Celebrating Cercignani's conjecture for the Boltzmann equation},
author = {Laurent Desvillettes and Clément Mouhot and Cédric Villani},
journal= {arXiv preprint arXiv:1009.4006},
year = {2012}
}
Comments
This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. added