Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A Cahn-Hilliard-Navier-Stokes model with delays

Pages: 2663 - 2685, Volume 21, Issue 8, October 2016      doi:10.3934/dcdsb.2016067

       Abstract        References        Full Text (438.7K)       Related Articles       

T. Tachim Medjo - Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, United States (email)

Abstract: In this article, we study a coupled Cahn-Hilliard-Navier-Stokes model with delays in a two-dimensional domain. The model consists of the Navier-Stokes equations for the velocity, coupled with an Cahn-Hilliard 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.

Keywords:  Cahn-Hilliard-Navier-Stokes, delays, strong solutions, stability.
Mathematics Subject Classification:  35Q30, 35Q35, 35Q72.

Received: November 2015;      Revised: July 2016;      Available Online: September 2016.