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

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arxiv 2502.18606 v1 pith:N5UGFVVQ submitted 2025-02-25 math.AP math-phmath.MP

José Antonio Carrillo , Shuchen Guo This is my paper · ORCID
classification math.APmath-phmath.MP
keywords equationfisherhierarchyinformationlandaumodelcompactnessconsider
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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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Cited by 2 Pith papers

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  1. Kac's Program for the Landau Equation

    math.AP 2025-06 conditional novelty 8.0 of 10

    The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L...

  2. Quantitative propagation of chaos for the Boltzmann equation with moderately soft potentials

    math.AP 2026-07 accept novelty 7.0 of 10

    For moderately soft potentials (-1<γ<0), the Kac particle empirical measure converges to the Boltzmann solution with quantitative W2 rate N^{-1/3}+N^{-ℓ(q,γ)}; first such rate.

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