Université Paris-Est Université Paris-Est - Marne-la-Vallée Université Paris-Est - Créteil Val-de-Marne Centre National de la Recherche Scientifique

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

03/06/2016 - 15:00 - 16:00
Salle de séminaires
XU Liping

We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials (γ ∈ (−1,0)) using the Wasserstein distance with quadratic cost. This in particular implies the uniqueness in the class of all weak solutions, assuming only that the initial condition has a finite entropy and a finite moment of sufficiently high order. We also consider the Nanbu N-stochastic particle system which approximates the weak solution. We use a probabilistic coupling method and give, under suitable assumptions on the initial condition, a rate of convergence of the empirical measure of the particle system to the solution of the Boltzmann equation for this singular interaction.