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Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules. (English) Zbl 1332.82075

Summary: 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 J. Fontbona et al. [Probab. Theory Relat. Fields 143, No. 3–4, 329–351 (2009; Zbl 1183.60037)] and of N. Fournier [Kinet. Relat. Models 2, No. 3, 451–464 (2009; Zbl 1197.82090)] 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.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
54C70 Entropy in general topology
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