A non-autonomous two-phase flow model with oscillating external force and its global attractor |
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Authors: | T Tachim Medjo |
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Institution: | Department of Mathematics, Florida International University, DM413B, University Park, Miami, FL 33199, USA |
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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. Assuming that the external force is singularly oscillating and depends on a small parameter ?, we prove the existence of the uniform global attractor A?. 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? as ? 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]. |
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Keywords: | 35Q30 35Q35 35Q72 |
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