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November  2017, 22(9): 3273-3294. doi: 10.3934/dcdsb.2017137

## A two-phase flow model with delays

 Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, USA

Received  September 2016 Revised  February 2017 Published  April 2017

In this article, we study a coupled Allen-Cahn-Navier-Stokes model with delays in a two-dimensional domain. The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. We prove the existence and uniqueness of the weak and strong solution when the external force contains some delays. We also discuss the asymptotic behavior of the weak solutions and the stability of the stationary solutions.

Citation: Theodore Tachim Medjo. A two-phase flow model with delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3273-3294. doi: 10.3934/dcdsb.2017137
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