庆祝Boltzmann方程的Cercignani猜想
偏微分方程分析
2012-02-22 v2 数学物理
泛函分析
math.MP
摘要
Cercignani猜想假设了稀薄气体动力学中Boltzmann非线性积分算子的熵与熵产生泛函之间存在线性不等式。与对数Sobolev不等式和谱隙不等式领域相关，该问题在过去十年中一直是稀薄气体趋近热力学平衡的数学理论复兴的核心。在这篇综述文章中，我们回顾了自20世纪80年代该猜想提出以来所获得的各种正面和负面结果。
引用
@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}
}
备注
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