Navier-Stokes-Cahn-Hilliard equations on evolving surfaces
Analysis of PDEs
2025-02-12 v3
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
@article{arxiv.2401.12044,
title = {Navier-Stokes-Cahn-Hilliard equations on evolving surfaces},
author = {Charles M. Elliott and Thomas Sales},
journal= {arXiv preprint arXiv:2401.12044},
year = {2025}
}
Comments
59 pages. Fixed even more typos, and corrected the long time existence result