Propagation of chaos for the Landau equation with very soft and Coulomb potentials

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1. Verfasser: Tabary, Côme
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Veröffentlicht: 2025
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author Tabary, Côme
author_facet Tabary, Côme
contents We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials using a tightness/uniqueness method. To claim uniqueness, we need high integrability estimates that we obtain by crucially exploiting the dissipation of the Fisher information at the level of the particle system. To be able to exploit these estimates as $N\rightarrow \infty$, we prove the affinity in infinite dimension of the entropy production and Fisher information dissipation (and other first and second-order versions of the Fisher information through a general theorem), results which were up to now only known for the entropy and the usual Fisher information.
format Preprint
id arxiv_https___arxiv_org_abs_2506_15795
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Propagation of chaos for the Landau equation with very soft and Coulomb potentials
Tabary, Côme
Analysis of PDEs
We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials using a tightness/uniqueness method. To claim uniqueness, we need high integrability estimates that we obtain by crucially exploiting the dissipation of the Fisher information at the level of the particle system. To be able to exploit these estimates as $N\rightarrow \infty$, we prove the affinity in infinite dimension of the entropy production and Fisher information dissipation (and other first and second-order versions of the Fisher information through a general theorem), results which were up to now only known for the entropy and the usual Fisher information.
title Propagation of chaos for the Landau equation with very soft and Coulomb potentials
topic Analysis of PDEs
url https://arxiv.org/abs/2506.15795