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. 2014. ⟨hal-00765621v2⟩