Modul: MAT675 PDE and Mathematical Physics

## Convergence of the weak coupling limit to the Landau equation for the truncated BBGKY hierarchy

Dr. Raphael Winter talk

Speaker invited by: Prof. Dr. Benjamin Schlein

**Date:** 28.03.19 **Time:** 14.00 - 15.00 **Room:** Y27H12

We show 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.