A non-autonomous two-phase flow model with oscillating external force and its global attractor

In this article, we consider a non-autonomous diffuse interface model for an isothermal incompressible two-phase flow in a two-dimensional bounded domain. Assuming that the external force is singularly oscillating and depends on a small parameter ϵϵ, we prove the existence of the uniform global attractor AϵAϵ. Furthermore, using the method similar to that of Chepyzhov and Vishik (2007) [22] in the case of the two-dimensional Navier–Stokes systems, we study the convergence of AϵAϵ as ϵϵ goes to zero. Let us mention that the nonlinearity involved in the model considered in this article is slightly stronger than the one in the two-dimensional Navier–Stokes system studied in Chepyzhov and Vishik (2007) [22].