Polynomial decay to equilibrium for the Becker-D\"oring equations

Abstract

This paper studies rates of decay to equilibrium for the Becker-D\"oring equations with subcritical initial data. In particular, polynomial rates of decay are established when initial perturbations of equilibrium have polynomial moments. This is proved by using new dissipation estimates in polynomially weighted $\ell^1$ spaces, operator decomposition techniques from kinetic theory, and interpolation estimates from the study of travelling waves.