From a non-Markovian system to the Landau equation

Abstract

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, which 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.

References in corpus (3)

• Entropy dissipation estimates for the Landau equation in the Coulomb case and applications
• The Boltzmann-Grad Limit of a Hard Sphere System: Analysis of the Correlation Error
• Book review: From Newton to Boltzmann: Hard Spheres and Short-range Potentials, by Isabelle Gallagher, Laure Saint-Raymond and Benjamin Texier

Cited by in corpus (2)

• The two-particle correlation function for systems with long-range interactions
• Subdynamics of a many-particle classical system driven from an equilibrium state by an external force