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arXiv · 1707.02274

Structure of correlations for the Boltzmann-Grad limit of hard spheres

Ryan Denlinger
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Abstract

We consider a gas of $N$ identical hard spheres in the whole space, and we enforce the Boltzmann-Grad scaling. We may suppose that the particles are essentially independent of each other at some initial time; even so, correlations will be created by the dynamics. We will prove a structure theorem for the correlations which develop at positive time. Our result generalizes a previous result which states that there are phase points where the three-particle marginal density factorizes into two-particle and one-particle parts, while further factorization is impossible. The result depends on uniform bounds which are known to hold on a small time interval, or globally in time when the mean free path is large.

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Ryan Denlinger. 2017-07-07. Structure of correlations for the Boltzmann-Grad limit of hard spheres. https://doi.org/10.1063/1.4998194

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