Unique strong and attractor of a three dimensional globally modified Cahn-Hilliard-Navier-Stokes model

Abstract

In this article, we study a globally modified Cahn–Hilliard–Navier–Stokes system in a three-dimensional domain. The model consists of the globally modified Navier–Stokes equations proposed, coupled with a Cahn–Hilliard model. We prove the existence and uniqueness of strong solutions. Using the flattening property, we also prove the existence of global attractors for the model. Using a limiting argument, we derive the existence of bounded entire weak solutions for the three-dimensional coupled Cahn–Hilliard–Navier–Stokes system with time-independent forcing.

Keywords:

• Cahn–Hilliard–Navier–Stokes
• globally modified
• strong solutions
• global 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.