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arXiv · 2212.04392

Long time validity of the linearized Boltzmann equation for hard spheres: a proof without billiard theory

Corentin Le Bihan
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Abstract

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.

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Corentin Le Bihan. 2022-12-08. Long time validity of the linearized Boltzmann equation for hard spheres: a proof without billiard theory. https://arxiv.org/abs/2212.04392

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