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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2019

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

Résumé

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.
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Dates et versions

hal-01665338 , version 1 (15-12-2017)
hal-01665338 , version 2 (17-12-2018)
hal-01665338 , version 3 (06-03-2019)

Identifiants

Citer

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, 2019, 233 (2), pp.837-866. ⟨10.1007/s00205-019-01369-6⟩. ⟨hal-01665338v3⟩
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