A Cahn-Hilliard-Navier-Stokes model with delays

In this article, we study a coupled Cahn-Hilliard-Navier-Stokes model with delaysin a two-dimensional domain. The model consists of the Navier-Stokes equations for thevelocity, coupled with an Cahn-Hilliard model for theorder (phase) parameter.We prove the existence and uniqueness of the weak andstrong solution when the external force contains some delays. Wealso discuss the asymptotic behavior of the weak solutions and thestability of the stationary solutions.