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arXiv · 2508.10697

From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method

Shuchen Guo
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Abstract

We study the Kac particle model for the space-homogenous Landau equation with hard potentials. By showing a sharper Povzner-type inequality, we obtain the uniform-in-time and uniform-in-N propagation of exponential moment for the first marginal of the solution of the many-particle Liouville equation. This key property enables us to show the uniqueness of weak solutions of the corresponding infinite Landau hierarchy by coupling method. As a result, we prove the propagation of chaos for the Landau equation with hard potentials.

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Shuchen Guo. 2025-08-14. From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method. https://arxiv.org/abs/2508.10697

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