Long-Time Correlations For A Hard-Sphere Gas At Equilibrium

Thierry Bodineau (1) , Isabelle Gallagher (2, 3) , Laure Saint-Raymond (4) , Sergio Simonella (4, 5)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 UPD7 - Université Paris Diderot - Paris 7
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
5 CNRS - Centre National de la Recherche Scientifique

It has been known since Lanford [22] that the dynamics of a hard sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilibrium. In this paper, we introduce a weak convergence method coupled with a sampling argument to prove that the covariance of the fluctuation field around equilibrium is governed by the linearized Boltzmann equation globally in time (including in diffusive regimes). This method is much more robust and simple than the one devised in [4] which was specific to the 2D case.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Probabilités [math.PR]

Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella. Long-Time Correlations For A Hard-Sphere Gas At Equilibrium. Communications on Pure and Applied Mathematics, inPress, ⟨10.48550/arXiv.2012.03813⟩. ⟨hal-03041164v2⟩