CUTOFF ESTIMATES FOR THE LINEARIZED BECKER-DORING EQUATIONS

This paper continues the authors' previous study [R. Murray and R. Pego, SIAM J. Math. Anal., 48:2819-2842, 2016] of the trend toward equilibrium of the Becker Doring equations with subcritical mass, by characterizing certain fine properties of solutions to the linearized equation. In particular, we partially characterize the spectrum of the linearized operator, showing that it contains the entire imaginary axis in polynomially weighted spaces. Moreover, we prove detailed cutoff estimates that establish upper and lower bounds on the lifetime of a class of perturbations to equilibrium.