Kinetic and Related Models (KRM)

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

Pages: 1 - 49, Volume 9, Issue 1, March 2016      doi:10.3934/krm.2016.9.1

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Kleber Carrapatoso - CEREMADE, Université Paris-Dauphine, UMR CNRS 7534, F-75775 Paris, France (email)

Abstract: We prove a quantitative propagation of chaos and entropic 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 [9] and Fournier [10] 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.

Keywords:  Chaos, entropic chaos, propagation of chaos, Landau equation, grazing collisions, Maxwellian molecules, trend to equilibrium.
Mathematics Subject Classification:  Primary: 82C40, 76P05, 60K35, 54C70.

Received: April 2014;      Revised: September 2015;      Available Online: October 2015.