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

Abstract

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 ϵ , we prove the existence of the uniform global attractor A ϵ . 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 A ϵ as ϵ 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].