A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow
Abstract
We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only assumed that the divergences of the two fluxes --- but not necessarily the fluxes themselves --- annihilate each other. Our main result is a rigorous proof of existence of weak solutions. The starting point is the formal representation of the dynamics as a constrained gradient flow in the Wasserstein metric. We then show that time-discrete approximations by means of the incremental minimizing movement scheme converge to a weak solution in the limit. Further, we compare the non-local model to the classical Cahn-Hilliard model in numerical experiments. Our results illustrate the significant speed-up in the decay of the free energy due to the higher degree of freedom for the velocity fields.
Keywords
Cite
@article{arxiv.1712.06446,
title = {A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow},
author = {Clément Cancès and Daniel Matthes and Flore Nabet},
journal= {arXiv preprint arXiv:1712.06446},
year = {2019}
}