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Convergence to the Landau equation from the truncated BBGKY hierarchy in the weak-coupling limit

Raphael Winter 1
1 UMPA
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
Abstract : We consider the evolution of the one-particle function in the weak-coupling limit in three space dimensions, obtained by truncating the BBGKY hierarchy under a propagation of chaos approximation. For this dynamics, we rigorously show the convergence to a solution of the Landau equation, keeping the full singularity of the Landau kernel. This resolves the issue arising from [10], where the singular region has been removed artificially. Since the singularity appears in the Landau equation due to the geometry of particle interactions, it is an intrinsic physical property of the weak-coupling limit which is crucial to the understanding of the transition from particle systems to the Landau equation.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-02408309
Contributor : Raphael Winter <>
Submitted on : Friday, December 13, 2019 - 12:08:02 AM
Last modification on : Monday, January 13, 2020 - 1:18:39 AM

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  • HAL Id : ensl-02408309, version 1
  • ARXIV : 1905.05021

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Raphael Winter. Convergence to the Landau equation from the truncated BBGKY hierarchy in the weak-coupling limit. 2019. ⟨ensl-02408309⟩

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