Propagation of chaos for the spatially homogeneous landau equation for maxwellian molecules

Kleber Carrapatoso

doi:10.3934/krm.2016.9.1

Propagation of chaos for the spatially homogeneous landau equation for maxwellian molecules

Kleber Carrapatoso

Université Paris Dauphine
Université Paris-Saclay

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

9 Citations (Scopus)

Résumé

We prove a quantitative propagation of chaos and entropic chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Guérin and Méléard [9] and Fournier [10] where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.

langue originale	Anglais
Pages (de - à)	1-49
Nombre de pages	49
journal	Kinetic and Related Models
Volume	9
Numéro de publication	1
Les DOIs	https://doi.org/10.3934/krm.2016.9.1
état	Publié - 1 janv. 2016
Modification externe	Oui

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title = "Propagation of chaos for the spatially homogeneous landau equation for maxwellian molecules",

abstract = "We prove a quantitative propagation of chaos and entropic chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Gu{\'e}rin and M{\'e}l{\'e}ard [9] and Fournier [10] where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.",

keywords = "Chaos, Entropic chaos, Grazing collisions, Landau equation, Maxwellian molecules, Propagation of chaos, Trend to equilibrium",

author = "Kleber Carrapatoso",

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N2 - We prove a quantitative propagation of chaos and entropic chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Guérin and Méléard [9] and Fournier [10] where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.

AB - We prove a quantitative propagation of chaos and entropic chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Guérin and Méléard [9] and Fournier [10] where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.

KW - Chaos

KW - Entropic chaos

KW - Grazing collisions

KW - Landau equation

KW - Maxwellian molecules

KW - Propagation of chaos

KW - Trend to equilibrium

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DO - 10.3934/krm.2016.9.1

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JF - Kinetic and Related Models

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Propagation of chaos for the spatially homogeneous landau equation for maxwellian molecules

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