Celebrating Cercignani's conjecture for the Boltzmann equation
arXiv:1009.4006 · doi:10.3934/krm.2011.4.277
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.
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
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Cited by in corpus (8)
- Exponential convergence to equilibrium for subcritical solutions of the Becker-Döring equations
- Entropy dissipation estimates for the linear Boltzmann operator
- Trend to Equilibrium for the Becker-Döring Equations: An Analogue of Cercignani's Conjecture
- Rescaled Objective Solutions of Fokker-Planck and Boltzmann equations
- About the use of entropy production for the Landau-Fermi-Dirac equation
- Entropy production in nonlinear recombination models
- From Boltzmann to random matrices and beyond
- Rigorous study of the equilibria of collision kernels appearing in the theory of weak turbulence