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

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arxiv 2409.04031 v1 pith:FEXUZVCU submitted 2024-09-06 math.PR math-phmath.APmath.MP

Chenguang Liu , Liping Xu , An Zhang This is my paper · ORCID
classification math.PRmath-phmath.APmath.MP
keywords hardboltzmannequationparticlepotentialsratesystemassumption
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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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  1. Quantitative propagation of chaos for the Boltzmann equation with moderately soft potentials

    math.AP 2026-07 accept novelty 7.0 of 10

    For moderately soft potentials (-1<γ<0), the Kac particle empirical measure converges to the Boltzmann solution with quantitative W2 rate N^{-1/3}+N^{-ℓ(q,γ)}; first such rate.

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