# Topics in Non-Collisional Kinetic Theory Spring 2021

- Lecturers
- Ludovic Cesbron, Mikaela Iacobelli
- Coordinator
- Antoine Gagnebin
- Lectures
- Mon 2:15-4:00pm, online
- First Lecture
- 01.03.2021
- Office Hours
- Tue. 10-12am, Thur. 2:15-4:15pm
- Zoom Meeting Room
- ID 914 4700 2409

## Syllabus

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:

- Transport equations
- Characteristic method
- Weak solutions to conservative transport equations

- Kinetic theory of Plasmas
- Mean field limit
- From particles model to Vlasov-Poisson
- Dobrushin’s stability theorem

- The Cauchy problem for Vlasov-Poisson

## Prerequisites

- Required: Notions in functional analysis, differential equations and Lebesgue integration
- Optional: Distribution theory, Sobolev spaces, notions in elliptic PDEs

## Rules of the Seminar Class

To obtain the credits for the seminar each student must:

- Give two 40min presentations on assigned topics. One during the first half of the semester and one during the second half.
- Submit the visual support you prepared for your seminar (pdf, beamer, written notes...) so that they can be uploaded on this webpage
- Attend the lectures and follow your classmates' seminars

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

Elementary Inequalities

## Literature

Lecture Notes

Extended Litterature

- The Cauchy Problem in Kinetic Theory, by R.T. Glassey, Society for Industrial and Applied Mathematics, 1996
- On the Dynamics of Large Particle Systems in the Mean Field Limit, by F. Golse , arxiv preprint 1301.5494, 2013
- Partial Differential Equations, L.C. Evans, American Mathematical Society, 2010
- Partial Differential Equations in Action, S. Salsa, Springer International Publishing, 2015
- Functional Analysis, T. Bühler and D.A. Salamon, American Mathematical Society, 2018
- Topics in Optimal Transport, C. Villani, American Mathematical Society, 2003