Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation

Xuanrui Feng; Chenguang Liu; Zhenfu Wang

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arXiv · 2608.29815

Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation

Xuanrui Feng·Chenguang Liu·Zhenfu Wang

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Abstract

We prove uniform-in-time quantitative relative entropy estimates for Kac's particle approximation of the three-dimensional spatially homogeneous Landau equation for Maxwellian molecules. Using the relative entropy method and logarithmic derivative estimates, we obtain a finite-time normalized entropy bound of order $N^{-1/2}$. The proof relies on explicit covariance identities and a new law-of-large-numbers estimate for the particle system using a new duality method. The uniform-in-time propagation of chaos is derived from an interpolation with an algebraic relaxation estimate toward equilibrium.

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Xuanrui Feng, Chenguang Liu, Zhenfu Wang. 2026-08-30. Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation. https://arxiv.org/abs/2608.29815

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