An Introduction to Mean-Field Limits for Vlasov Equations
Spring 2022

Prof. Dr. Mikaela Iacobelli, Dr. Alexandre Rege
Antoine Gagnebin
Mon 2:15-4:00pm, ML J 37.1
First Lecture
Office Hours
TBD on zoom
Zoom Meeting Room
ID 570 479 7608
Course Catalogue


This seminar will investigate the relation between "exact" microscopic models that govern large particle systems' evolution and a specific type of approximate models known in Statistical Mechanics as "mean-field equations". Roughly speaking, a mean-field equation is a model that describes the evolution of a typical particle subject to the collective interaction created by a large number of other, identical particles. The most famous example of mean-field equation is the Vlasov-Poisson equation.

The mathematical justification of the mean-field limit involves very different ideas and methods. This course aims to give an introductory description of the classical approaches to the problem of the mean-field limit in mathematical analysis.

In particular, the intent is to learn essential tools and techniques for studying Partial Differential Equations while applying them to Vlasov equations.

Content of the course:


Rules of the Seminar Class

To obtain the credits for the seminar each student must:

The topics and associated parts of the Lecture notes will be assigned to student on the first lecture.

Seminar Weeks

28.02 Introduction to the seminar Prof. Dr. Mikaela Iacobelli
07.03 Tools for PDE's Antoine Gagnebin
14.03 Break
21.03 Transport Equations with Constant Coefficients
Transport Equations with Variable Coefficients
Isabella Brovelli Chap 2 Sect 2.1 & 2.2 [FG2013]
28.03 Conservative Transport and Weak Solutions Adrian Dawid Chap 2 Sect 2.3 [FG2013 ]
04.04 General formalism in classical mechanics
Mean field characteristic flow
David LenzeChap 3 Sect 3.1 & 3.2 [FG2013]
(Stop before Theorem 3.2.2)
11.04 Mean field characteristic flow
The Monge-Kantorovich distance
Dobrushin’s estimate
Fatime RasitiChap 3 Sect 3.2, 3.3.1 & 3.3.2 [FG2013]
(Start with Theorem 3.2.2)
18.04 Easter Monday
25.04 Sechseläuten afternoon off
02.05 The mean field limit
On the choice of the initial data
Yuxiu Zhang Chap 3 Sect 3.3.3 & 3.3.4 [FG2013]


Lecture Notes Extended Litterature