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.
Complete list of metadatas

Cited literature [42 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01665338
Contributor : Clément Cancès <>
Submitted on : Wednesday, March 6, 2019 - 11:08:20 AM
Last modification on : Saturday, July 20, 2019 - 7:30:43 PM

File

CH_JKO_final.pdf
Files produced by the author(s)

Identifiers

Citation

Clément Cancès, Daniel Matthes, Flore Nabet. A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow. Archive for Rational Mechanics and Analysis, Springer Verlag, 2019, 233 (2), pp.837-866. ⟨10.1007/s00205-019-01369-6⟩. ⟨hal-01665338v3⟩

Share

Metrics

Record views

242

Files downloads

273