A two-phase flow model with delays

Theodore Tachim Medjo

doi:10.3934/dcdsb.2017137

Article Contents

2017, Volume 22, Issue 9: 3273-3294. Doi: 10.3934/dcdsb.2017137

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A two-phase flow model with delays

Theodore Tachim Medjo

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

Received: September 2016

Revised: February 2017

Published: October 2017

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Abstract

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.

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Mathematics Subject Classification: 35Q30, 35Q35, 35Q72.

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