# American Institute of Mathematical Sciences

October  2012, 32(10): 3665-3690. doi: 10.3934/dcds.2012.32.3665

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

 1 Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, United States

Received  April 2011 Revised  March 2012 Published  May 2012

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].
Citation: T. Tachim Medjo. Averaging of an homogeneous two-phase flow model with oscillating external forces. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3665-3690. doi: 10.3934/dcds.2012.32.3665
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##### References:
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