Averaging of an homogeneous two-phase flow model withoscillating external forces

T. Tachim Medjo

doi:10.3934/dcds.2012.32.3665

Article Contents

2012, Volume 32, Issue 10: 3665-3690. Doi: 10.3934/dcds.2012.32.3665

This issue Previous Article Cone-fields without constant orbit core dimension Next Article Blow-up behavior of solutions to a parabolic-elliptic system on higher dimensional domains

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

T. Tachim Medjo^1,

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

Received: March 31, 2011

Revised: February 29, 2012

Published: September 2012

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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. 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].

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Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 35Q72.

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