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Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation
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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BibTeX
@misc{feng2026uniformintime,
title = {{Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation}},
author = {Xuanrui Feng and Chenguang Liu and Zhenfu Wang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29815},
eprint = {2608.29815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29815},
}
RIS
TY - UNPB
TI - Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation
AU - Xuanrui Feng
AU - Chenguang Liu
AU - Zhenfu Wang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29815
UR - https://arxiv.org/abs/2608.29815
AB - 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.
ER -