Quantitative uniform propagation of chaos for Maxwell molecules

Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials

“…Then, Fournier-Mischler [13] proved the propagation of chaos at rate N −1/4 for the Nanbu system and for hard potentials without cutoff (γ ∈ [0, 1] and ν ∈ (0, 1)). Finally, as mentioned in Section 1.5, Cortez-Fontbona [4] used two coupling techniques for Kac's binary interaction system and obtained a uniform in time estimate for the Boltzmann equation with Maxwell molecules (γ = 0) under some suitable moments assumptions on the initial datum. Let us mention that the time-uniformity uses the recent nice results of Rousset [27].…”

“…It is thus impossible to simulate it directly. For this reason, we will study a truncated version of Nanbu's particle system applying a cutoff procedure as [13], who were studying the Nanbu system for hard potentials and Maxwell molecules, and [4], who were dealing with the Kac system for Maxwell molecules. Our particle system with cutoff corresponds to the generator L N,K defined, for any bounded Lipschitz function φ : (R 3 ) N → R and v = (v 1 , ..., v N ) ∈ (R 3 ) N , by…”