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

Liping Xu, University of Washington
Monday, May 14, 2018 - 2:30pm to 3:30pm
SMI 304

Abstract: 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 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.

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