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Averaging of an homogeneous two-phase flow model with oscillating external forces

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  • In this article, we consider a non-autonomous diffuse interface model for an isothermal incompressible two-phase flow in a two-dimensional bounded domain. We assume that the external force is singularly oscillating and depends on a small parameter $ \epsilon. $ We prove the existence of the uniform global attractor $A^{\epsilon}. $ Furthermore, using the method of [13] in the case of the two-dimensional Navier-Stokes systems, we study the convergence of $A^{\epsilon} $ as $ \epsilon $ 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 [13].
    Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 35Q72.

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