Topics in Non-Collisional Kinetic Theory Spring 2021

Ludovic Cesbron, Mikaela Iacobelli
Antoine Gagnebin
Mon 2:15-4:00pm, online
First Lecture
Office Hours
Tue. 10-12am, Thur. 2:15-4:15pm
Zoom Meeting Room
ID 914 4700 2409


This class is an introduction to the mathematical study of models from the Kinetic Theory of Plasmas. The intent is to learn essential tools and techniques for the study of Partial Differential Equations while applying them to some of the most important equations of Kinetic Theory: Vlasov equations.

Content of the course:


Rules of the Seminar Class

To obtain the credits for the seminar each student must:

Students are encouraged to work in pairs in order for the two presentations given during a Lecture to be coordinated and complementary. We strongly advise the students to do a mock presentation with their partner to ensure that the time limit of 40 minutes is respected and that the two presentations are clear and well-structured.

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

Exercise classes

01.03 Tools for PDEs A. Gagnebin Functional Analysis II, Prof. Carlotto
08.03Introduction to Kinetic Theory Dr. L. Cesbron Chapter 1 [FG2013]
15.03Transport Equations with Constant Coefficients
Transport Equations with Variable Coefficients
M. Planincic
A. Aydin
Chap 2 Sect 2.1-2.2 [FG2013]
22.03 Conservative Transport and Weak Solutions (Part 1)
Conservative Transport and Weak Solutions (Part 2)
C. Naiaretti
J. Junné
Chap 2 Sect 2.3 [FG2013 ]
29.03 General formalism in classical mechanics
Mean field characteristic flow
A. Hirschi Chap 3 Sect 3.1-3.2 [FG2013]
12.04 Dobrushin’s stability estimate and the mean field limit A. Gagnebin Chap 3 Sect 3.3 [FG2013]
03.05 The Vlasov-Poisson Equation and Elementary Inequalities A. Gagnebin Chap 4 Sect 4.1 [FG2013]
10.05 The approximate Vlasov-Poisson system J. Junné Chap 4 Sect 4.2.1 [FG2013]
17.05 Convergence to the Vlasov-Poisson system M. Planincic Chap 4 Sect 4.2.2 [FG2013]
31.06 Propagation of Moments in Dimension 2 + Step 1 of C1 Regularity
Propagation of C1 Regularity in Dimensions 2 and 3
C. Naiaretti
A. Aydin
Chap 4 Sect 4.3 & 4.5 [FG2013]
Elementary Inequalities


Lecture Notes Extended Litterature