"Landau damping and plasma echoes''
Abstract: The talk presents an elementary proof of the nonlinear
Landau damping for analytic and Gevrey data, that was first obtained
by Mouhot and Villani and subsequently extended by Bedrossian,
Masmoudi, and Mouhot, coupled with a presentation of echo solutions to
the classical Vlasov-Poisson system which in particular exhibit an
infinite cascade of echoes of smaller and smaller amplitude. The
constructed echo solutions do not belong to the analytic or Gevrey
classes studied by Mouhot and Villani, but do, nonetheless, exhibit
damping phenomena for large times. This is a joint work with Emmanuel
Grenier (ENS Lyon) and Igor Rodnianski (Princeton).