Modul: MAT675 PDE and Mathematical Physics

## Asymptotics for the Hartree equation

Anne-Sophie de Suzzoni talk

Speaker invited by: Prof. Dr. Benjamin Schlein

**Date:** 08.11.18 **Time:** 15.00 - 16.00 **Room:** Y27H46

In this talk, we will present one model (in the mean field limit) for large systems of particles interacting via a potential $w$. This model is a Hartree equation on random fields in $\R^d$ that admits equilibria related to thermodynamical equilibria. We study the asymptotic stability of these equilibria. One issue that arises is the fact that these equilibria are not localised in space, their laws are invariant by translation in space. We prove a scattering result around these equilibria under some assumptions on $w$. The proof is based on a high frequency/low frequency analysis and a reformulation of the problem.