Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Feng, Xuanrui, Liu, Chenguang, Wang, Zhenfu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5053629486, G590270663
OpenAlex ID: W7204866282