Navier–Stokes–Cahn–Hilliard equations on evolving surfaces
Charles M. Elliott
University of Warwick, Coventry, UKThomas Sales
University of Warwick, Coventry, UK

Abstract
We derive a system of equations which can be seen as an evolving surface version of the diffuse interface “Model H” of Hohenberg and Halperin (1977). We then consider the well-posedness for the corresponding (tangential) system when one prescribes the evolution of the surface. Well-posedness is proved for smooth potentials in the Cahn–Hilliard equation with polynomial growth, and also for a thermodynamically relevant singular potential.
Cite this article
Charles M. Elliott, Thomas Sales, Navier–Stokes–Cahn–Hilliard equations on evolving surfaces. Interfaces Free Bound. 27 (2025), no. 2, pp. 285–348
DOI 10.4171/IFB/528