A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

Clément Cancès (1, 2) , Daniel Matthes (3) , Flore Nabet (4)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We study a so-called non-local Cahn-Hilliard model obtained as a constrained Wasser-stein gradient flow of some Ginzburg-Landau energy. When compared to the more classical local degenerate Cahn-Hilliard model studied in [C. M. Elliott and H. Garcke, SIAM J. Math. Anal., 27(2):404–423, 1996], the non-local model appears to take advantage of a larger flexibility on the phase fluxes to dissipate faster the energy, as confirmed by numerical simulations. We prove the existence of a solution to non-local problem by proving the convergence of the JKO minimizing movement scheme.

Mots clés: constrained Wasserstein gradient flow; Cahn-Hilliard type system; Multiphase flow

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Clément Cancès, Daniel Matthes, Flore Nabet. A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow. 2017. ⟨hal-01665338v1⟩