RATE OF CONVERGENCE OF THE NANBU PARTICLE SYSTEM FOR HARD POTENTIALS AND MAXWELL MOLECULES

• 成果类型: Article
• 署名作者: Fournier, Nicolas; Mischler, Stephane
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP983
• 发表日期: 2016
• 页码: 589-627
• 关键词: homogeneous boltzmann-equation; kacs chaos; uniqueness; STABILITY; entropy; approximation; propagation

摘要

We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials and Maxwell molecules. We establish a rate of propagation of chaos of the particle system to the unique solution of the Boltzmann equation. More precisely, we estimate the expectation of the squared Wasserstein distance with quadratic cost between the empirical measure of the particle system and the solution to the Boltzmann equation. The rate we obtain is almost optimal as a function of the number of particles but is not uniform in time.