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arXiv · 2502.18606

From Fisher information decay for the Kac model to the Landau-Coulomb hierarchy

José Antonio Carrillo·Shuchen Guo
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Abstract

We consider the Kac model for the space-homogeneous Landau equation with the Coulomb potential. We show that the Fisher information of the Liouville equation for the unmodified $N$-particle system is monotonically decreasing in time. The monotonicity ensures the compactness to derive a weak solution of the Landau hierarchy.

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José Antonio Carrillo, Shuchen Guo. 2025-02-25. From Fisher information decay for the Kac model to the Landau-Coulomb hierarchy. https://arxiv.org/abs/2502.18606

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