# Nonlinear echoes and Landau damping with insufficient regularity

Monday, September 19, 2016 -

4:00pm to 5:00pm

In this talk, we will discuss recent advances towards understanding the regularity hypotheses in the theorem of Mouhot and Villani on Landau damping near equilibrium for the Vlasov-Poisson equations. We show that, in general, their theorem cannot be extended to any Sobolev space on the 1D torus. This is demonstrated by constructing arbitrarily small solutions with a sequence of nonlinear oscillations, known as plasma echoes, which damp at a rate arbitrarily slow compared to the linearized Vlasov equations. Some connections with hydrodynamic stability problems will be discussed if time permits.

Speaker:

Jacob Bedrossian

University of Maryland

Event Location:

Fine Hall 214