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From a non-Markovian system to the Landau equation. (English) Zbl 1433.60067

Summary: In this paper, we prove that in macroscopic times of order one, the solutions to the truncated BBGKY hierarchy (to second order) converge in the weak coupling limit to the solution of the nonlinear spatially homogeneous Landau equation. The truncated problem describes the formal leading order behavior of the underlying particle dynamics, and can be reformulated as a non-Markovian hyperbolic equation that converges to the Markovian evolution described by the parabolic Landau equation. The analysis in this paper is motivated by Bogolyubov’s derivation of the kinetic equation by means of a multiple time scale analysis of the BBGKY hierarchy.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
82C22 Interacting particle systems in time-dependent statistical mechanics
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