论文标题
线性化玻尔兹曼方程的长期有效性硬球：没有台球理论的证明
Long time validity of the linearized Boltzmann equation for hard spheres: a proof without billiard theory
论文作者
论文摘要
我们研究了热平衡下硬球系统的时空波动，并证明协方差会在低密度极限（全球范围内）以低密度极限为单位的线性化玻尔兹曼方程的溶液。通过对硬球的分散系统的回忆数进行统一的界限（例如[9]中提供），该结果以前是在[7]中获得的。我们提供了一个具有实质性差异的独立证明，这不使用这种几何结果。这可以被认为是旨在得出稀有气体波动理论的程序的第一步，其相互作用势与硬球不同。
We study space-time fluctuations of a hard sphere system at thermal equilibrium, and prove that the covariance converges to the solution of a linearized Boltzmann equation in the low density limit, globally in time. This result has been obtained previously in [7], by using uniform bounds on the number of recollisions of dispersing systems of hard spheres (as provided for instance in [9]). We present a self-contained proof with substantial differences, which does not use this geometric result. This can be regarded as the first step of a program aiming to derive the fluctuation theory of the rarefied gas, for interaction potentials different from hard spheres.
