We consider coarsening dynamics associated with a Burgers–Cahn–Hilliard system modeling two-phase flow in one space dimension. Our emphasis is on the effect that coupling between the phase and fluid dynamics has on coarsening rates, and on the mechanisms driving this effect. We begin our analysis by establishing global well-posedness of the system under consideration, focusing on both periodic and physical boundary conditions. After reviewing our previous work on coarsening dynamics for the non-coupled Cahn–Hilliard equation, we use computational simulations to study how these dynamics are affected by appropriate choices of couplings with the viscous Burgers equation. We conclude that the effect of coupling on energy decay and coarsening rate is quite substantial.
Howard et al. (Fri,) studied this question.