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Title: From microscopic dynamics to kinetic equations
Keywords: kinetic equations
scaling limits
Boltzmann equation
Landau equation
Vlasov-Poisson system
Kac model
Issue Date: 19-Dec-2012
Abstract: Starting from a system of N particles at a microscopic scale, we describe different scaling limits which lead to kinetic equations in a macroscopic regime: the low-density limit, the weak-coupling limit, the grazing collision limit and the mean-field limit. A particular relevance is given to the rigorous derivation of the Boltzmann equation (starting from a system of N particles interacting via a short range potential) and to a consistency result concerning the Landau equation. A Kac's model for the Landau equation is presented as well. The last part of the work is dedicated to the Vlasov-Poisson system, in particular we discuss the Cauchy problem related to this equation in presence of a point charge.

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