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

TL;DR

This paper establishes polynomial decay rates to equilibrium for the Becker-Döring equations with subcritical initial data, using new dissipation estimates, operator decomposition, and interpolation techniques.

Contribution

It introduces novel dissipation estimates and operator decomposition methods to prove polynomial decay in weighted spaces for the Becker-Döring equations.

Findings

Polynomial decay rates are proven for subcritical initial data.

New dissipation estimates in weighted $ ext{ell}^1$ spaces are developed.

Operator decomposition techniques from kinetic theory are applied.

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.