Landau damping: Gevrey regularity and paraproducts

Non-equilibrium Dynamics and Random Matrices
Topic:Landau damping: Gevrey regularity and paraproducts
Speaker:Clément Mouhot
Affiliation:University of Cambridge
Date:Wednesday, April 30
Time/Room:11:00am - 12:00pm/S-101
Video Link:http://video.ias.edu/nedrm/2014/0430-Cl%C3%A9mentMouhot

We present the key ideas of a new proof of Landau damping for the Vlasov-Poisson equation obtained in a joint work with Bedrossian and Masmoudi. This nonlinear transport equation is a fundamental model for describing self-interacting plasmas or galaxies, and Landau damping is a nonlinear stability mechanism based on phase mixing. The new method does not use a Newton scheme and seems to capture a critical Gevrey regularity for the damping. Moreover its greater flexibility should open the way to further work, and we will finish by sketching some open questions.