Attractors for a two-phase flow model with delays. (Q504273)

In this article, a coupled Allen-Cahn-Navier-Stokes model with delays is studied in a two-dimensional bounded domain. The model consists of the Navier-Stokes equations for the velocity, coupled with a Allen-Cahn model for the order (phase) parameter, and describes homogeneous incompressible two-phase flow with singularly oscillating forces. The external forcing terms contain some delays, i.e., depend on the history of the solution on a finite time interval. This leads to an application of the theory of pullback attractors, which is adapted to the model in question. The existence of bounded (pullback) absorbing sets is proved, and, finally, the existence of a unique uniformly bounded pullback attractors for the associated two-parameter semigroups (processes) is shown.