Clement Mouhot (Cambridge)
Landau damping: Gevrey regularity and paraproducts
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.