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.
Classification :
35K59, 35Q35, 35K67
Mots-clés :
evolving surface, Navier–Stokes–Cahn–Hilliard, Model H
Affiliations des auteurs :
Charles M. Elliott
1
;
Thomas Sales
1
1
University of Warwick, Coventry, UK
Charles M. Elliott; Thomas Sales. Navier–Stokes–Cahn–Hilliard equations on evolving surfaces. Interfaces and free boundaries, Tome 27 (2025) no. 2, pp. 285-348. doi: 10.4171/ifb/528
@article{10_4171_ifb_528,
author = {Charles M. Elliott and Thomas Sales},
title = {Navier{\textendash}Stokes{\textendash}Cahn{\textendash}Hilliard equations on evolving surfaces},
journal = {Interfaces and free boundaries},
pages = {285--348},
year = {2025},
volume = {27},
number = {2},
doi = {10.4171/ifb/528},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/528/}
}
TY - JOUR
AU - Charles M. Elliott
AU - Thomas Sales
TI - Navier–Stokes–Cahn–Hilliard equations on evolving surfaces
JO - Interfaces and free boundaries
PY - 2025
SP - 285
EP - 348
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/528/
DO - 10.4171/ifb/528
ID - 10_4171_ifb_528
ER -
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%A Charles M. Elliott
%A Thomas Sales
%T Navier–Stokes–Cahn–Hilliard equations on evolving surfaces
%J Interfaces and free boundaries
%D 2025
%P 285-348
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/528/
%R 10.4171/ifb/528
%F 10_4171_ifb_528
