Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions

Abstract

In this paper we develop a symmetry preserving method for the rigorous computation of stationary states of the Ohta-Kawasaki partial differential equation in three space dimensions. By preserving the relevant symmetries we achieve an enormous reduction in computational cost. This makes it feasible to construct computer-assisted proofs of complex three-dimensional structures. In particular, we provide the first existence proofs for both the double gyroid and body centered cubic packed sphere solutions to this problem