# Analysis Seminar

#### Landau damping and nonlinear echoes

Speaker: Jacob BEDROSSIAN, U. Maryland

Location: Warren Weaver Hall 1302

Date: Thursday, February 15, 2018, 11 a.m.

Synopsis:

In this talk we will discuss some of the intricacies of Landau
damping in the collisionless Vlasov equations and the weak collision limits
of Vlasov-Fokker-Planck equations. We will discuss the construction of
solutions to the Vlasov-Poisson equations on S x R which are arbitrarily
close to homogeneous equilibrium in Sobolev regularity but which display
arbitrarily long sequences of nonlinear oscillations known as plasma echoes.
In particular, these oscillations show that the collisionless linearization
is not accurate for long times in Sobolev regularity. Further, we show that
the inclusion of weak collisional effects suppress these plasma echoes and
make it possible to obtain Sobolev regularity results while not introducing
new hydrodynamic instabilities. Combined with the existing infinite
regularity results of Mouhot and Villani, these results together confirm
and refute a variety of conjectures made by both mathematicians and
physicists over the years regarding Landau damping near homogeneous
equilibrium.