LENARD-BALESCU CORRECTION TO MEAN-FIELD THEORY

Mitia Duerinckx (1, 2) , Laure Saint-Raymond (2)

1 ULB - Département de Mathématique [Bruxelles]
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

In the mean-field regime, the evolution of a gas of N interacting particles is governed in first approximation by a Vlasov type equation with a self-induced force field. This equation is conservative and describes return to equilibrium only in the very weak sense of Landau damping. However, the first correction to this approximation is given by the Lenard-Balescu operator, which dissipates entropy on the very long timescale O(N). In this paper, we show how one can derive rigorously this correction on intermediate timescales (of order O(N r) for r < 1), close to equilibrium.

Domaines: Equations aux dérivées partielles [math.AP]

Mitia Duerinckx, Laure Saint-Raymond. LENARD-BALESCU CORRECTION TO MEAN-FIELD THEORY. 2019. ⟨ensl-02389995⟩