Jacques Smulevici[a]
Vector field methods for kinetic equations
Pages: 245-306
Received: 28 April 2023
Accepted in revised form: 15 February 2024
Mathematics Subject Classification: 35Q83; 35M31.
Keywords: Vlasov and kinetic equations, vector field methods, Vlasov-Poisson system.
Authors address:
[a]: Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 place Jussieu, 75252 Paris, France
Abstract: The vector field method has been a central tool in the analysis of geometric wave equations since its earlier development by Klainerman in the 1980s. We give here an overview of vector field methods in the context of kinetic equations, with applications to classical systems, such as the Vlasov-Poisson system. These notes emanate from the lectures given by the author during the 11th Summer School on Methods and Models of Kinetic Theory, Pesaro, June 2022.