On the Glassey-Schaeffer Estimates for Linear Landau Damping

Abstract

I revisit Glassey and Schaeffer’s (1994) analysis of the decay rate for linear Landau damping. I show that their argument can be simplified and extended to a larger class of initial conditions by calculating explicitly the k → 0 limit of the propagator that determines the time-evolution of the solutions in Fourier space. I also show that the decay estimates for the propagator can be refined by considering a new small-k domain where the dispersion function is bounded away from zero. As a result, I obtain improved algebraic decay rates when the background Vlasov equilibrium decays as a power law as |v| → ∞.