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April 2018 Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials
Liping Xu
Ann. Appl. Probab. 28(2): 1136-1189 (April 2018). DOI: 10.1214/17-AAP1327

Abstract

We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials [$\gamma\in(-1,0)$] 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.

Citation

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Liping Xu. "Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials." Ann. Appl. Probab. 28 (2) 1136 - 1189, April 2018. https://doi.org/10.1214/17-AAP1327

Information

Received: 1 May 2016; Revised: 1 February 2017; Published: April 2018
First available in Project Euclid: 11 April 2018

zbMATH: 06897952
MathSciNet: MR3784497
Digital Object Identifier: 10.1214/17-AAP1327

Subjects:
Primary: 60K35, 82C40

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2018
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