2022/11/24 by Jacob Bedrossian, Bedrossian, Jacob
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies
paper · pdf · doi:10.48550/arxiv.2211.13707
openalex publication_date 2022/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In these short, rather informal, expository notes I review the current state of the field regarding the mathematics of Landau damping, based on lectures given at the CIRM Research School on Kinetic Theory, November 14--18, 2022. These notes are mainly on Vlasov-Poisson in (x,v) ∈ \mathbb Td × \mathbb Rd however a brief discussion of the important case of (x,v) ∈ \mathbb Rd × \mathbb Rd is included at the end. The focus will be nonlinear and these notes include a proof of Landau damping on (x,v) ∈ \mathbb Td × \mathbb Rd in the Vlasov--Poisson equations meant for graduate students, post-docs, and others to learn the basic ideas of the methods involved. The focus is also on the mathematical side, and so most references are from the mathematical literature with only a small number of the many important physics references included. A few open problems are included at the end. These notes are not currently meant for publication so they may not be perfectly proof-read and the reference list might not be complete. If there is an error or you have some references which you think should be included, feel free to send me an email and I will correct it when I get a chance.