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. 
Jacob Bedrossian
University of Maryland
Event Location: 
Fine Hall 214