Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials

Chenguang Liu; Liping Xu; An Zhang

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arXiv · 2409.04031

Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials

Chenguang Liu·Liping Xu·An Zhang

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Abstract

In this paper, we prove that the Kac stochastic particle system converges to the weak solution of the spatially homogeneous Boltzmann equation for hard potentials and hard spheres. We give, under the initial data with finite exponential moment assumption, an explicit rate of propagation of chaos in squared Wasserstein distance with quadratic cost by using a double coupling technique.

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Chenguang Liu, Liping Xu, An Zhang. 2024-09-06. Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials. https://arxiv.org/abs/2409.04031

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