Trajectory attractors for binary fluid mixtures in 3D

Abstract

Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered. They consist of the 3D incompressible Navier-Stokes equations, subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation. Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids. Using the trajectory approach, the authors prove the existence of the trajectory attractor for both systems.

Keywords

Navier-Stokes equations / Allen-Cahn equations / Cahn-Hilliard equations / Two-phase fluid flows / Longtime behavior / Trajectory attractors

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