A Brief Introduction to the Scaling Limits and Effective Equations in Kinetic Theory

Mario Pulvirenti,Sergio Simonella

doi:10.1007/978-3-030-67104-4_6

A Brief Introduction to the Scaling Limits and Effective Equations in Kinetic Theory

Mario Pulvirenti, Sergio Simonella

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https://doi.org/10.1007/978-3-030-67104-4_6

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Publication Date: Jan 1, 2021

Citations: 2

Affiliation: Sapienza University of Rome, University of L'Aquila, Unit of Mathematics, Pure and Applied, École Normale Supérieure de Lyon, French National Centre for Scientific Research

#Equations In Kinetic Theory #Classical Particle Systems + Show 8 more

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Abstract

AbstractThe content of these notes is based on a series of lectures given by the first author at HIM, Bonn, in May 2019. They provide the material for a short introductory course on effective equations for classical particle systems. They concern the basic equations in kinetic theory, written by Boltzmann and Landau, describing rarefied gases and weakly interacting plasmas respectively. These equations can be derived formally, under suitable scaling limits, taking classical particle systems as a starting point. A rigorous proof of this limiting procedure is difficult and still largely open. We discuss some mathematical problems arising in this context.KeywordsKinetic theoryPropagation of chaosScaling limitsBoltzmann and Landau equations

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