In this article, we study a coupled Allen-Cahn-Navier-Stokes model with delays in a two-dimensional domain. The model consists of the Navier-Stokes equations for the velocity, coupled with a Allen-Cahn model for the order (phase) parameter. We prove the existence of an attractor using the theory of pullback attractors.
T. Tachim Medjo. "Attractors for a two-phase flow model with delays." Differential Integral Equations 29 (11/12) 1071 - 1092, November/December 2016. https://doi.org/10.57262/die/1476369330