Celebrating Cercignani's conjecture for the Boltzmann equation

Details Celebrating Cercignani's conjecture for the Boltzmann equation Celebrating Cercignani's conjecture for the Boltzmann equation

2010-09-21

arxiv.org/abs/1009.4006v2

Kinetic and related models 4, 1 (2011) 277-294

Mathematics

Analysis of PDEs

This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of

Scientific paper

10.3934/krm.2011.4.277

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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