Pullback attractor of a three dimensional globally modified Cahn–Hilliard-Navier–Stokes model

Abstract

The existence and final fractal dimension of a pullback attractor in the space for a three dimensional system of a non-autonomous globally modified Cahn–Hilliard-Navier–Stokes model on a bounded domain is established under appropriate properties on the time depending forcing term. The model consists of the globally modified Navier–Stokes equations for the velocity, coupled with a Cahn–Hilliard equation for the order (phase) parameter. The existence of the pullback attractors is obtained using the flattening property. Furthermore, we prove that the fractal dimension in of the pullback attractor is finite.

Keywords:

• Cahn–Hilliard-Navier–Stokes
• globally modified
• strong solutions
• pullback attractor

AMS Subject Classifications:

• 35Q30
• 35Q35
• 35Q72

Acknowledgements

The author would like to thank the anonymous referees whose comments help to improve the content of this article.

Notes

No potential conflict of interest was reported by the author.