Nonlinear echoes and Landau damping with insufficient regularity

Nonlinear echoes and Landau damping with insufficient regularity

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Jacob Bedrossian, University of Maryland
Fine Hall 214

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.