On the Cahn-Hilliard-Oono-Navier-Stokes equations with singular potentials

Abstract

Our aim in this article is to prove the existence of solutions for a Cahn–Hilliard–Navier–Stokes system based on the Oono model and with singular potentials (and, in particular, the thermodynamically relevant logarithmic potentials). The Oono model was proposed in order to account for long-ranged (nonlocal) interactions, but also to simplify numerical simulations.

Keywords:

• Binary fluid
• Navier–Stokes equations
• Cahn–Hilliard–Oono equation
• singular potentials
• existence

AMS Subject Classifications:

• 35K55
• 35Q35
• 76D05

Acknowledgements

The authors wish to thank the referees for their careful reading of the manuscript and useful comments. This article was written while the first author was visiting the Institute for Scientific Computing and Applied Mathematics at Indiana University. He wishes to thank this institution for its warm hospitality.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Science Foundation [grant number NSF-DMS-1206438], [grant number NSF-DMS-1510249] and by the Research Fund of Indiana University.