On the cardinality of collisional clusters for hard spheres at low density

Mario Pulvirenti (1, 2) , Sergio Simonella (3, 4)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
3 CNRS - Centre National de la Recherche Scientifique
4 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We resume the investigation, started in [2], of the statistics of backward clusters in a gas of N hard spheres of small diameter ε. A backward cluster is defined as the group of particles involved directly or indirectly in the backwards-in-time dynamics of a given tagged sphere. We obtain an estimate of the average cardinality of clusters with respect to the equilibrium measure, global in time, uniform in ε, N for ε 2 N = 1 (Boltzmann-Grad regime).

Mots clés: Hard spheres; low-density gas; Boltzmann equation; backward cluster

Domaines: Mathématiques [math]

Mario Pulvirenti, Sergio Simonella. On the cardinality of collisional clusters for hard spheres at low density. Discrete and Continuous Dynamical Systems - Series A, 2021. ⟨hal-02614992v2⟩