Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules

Kleber Carrapatoso (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We prove a quantitative propagation of chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Guérin and Méléard \cite{FonGueMe} and Fournier \cite{Fournier} where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.

Mots clés: trend to equilibrium; Chaos; entropic chaos; propagation of chaos; Landau equation; grazing collisions; Maxwellian molecules; trend to equilibrium.

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Kleber Carrapatoso. Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules. Kinetic and Related Models , 2016, 9 (1), pp.1-49. ⟨10.3934/krm.2016.9.1⟩. ⟨hal-00765621v3⟩