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Chinese Annals of Mathematics, Series B

, Volume 31, Issue 5, pp 655–678 | Cite as

Trajectory attractors for binary fluid mixtures in 3D

  • Ciprian G. GalEmail author
  • Maurizio Grasselli
Article

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 

2000 MR Subject Classification

35B40 35B41 35K55 35Q35 76D05 76T99 

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Copyright information

© Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanoItaly

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