2017/12/18 by Clément Cancès, Cancès, Clément, Daniel Matthes +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #35K41 #35K65 #49J40 #76T99 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1712.06446
openalex publication_date 2017/12/18 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
We study a non-local version of the Cahn-Hilliard dynamics for phase\nseparation in a two-component incompressible and immiscible mixture with linear\nmobilities. In difference to the celebrated local model with nonlinear\nmobility, it is only assumed that the divergences of the two fluxes --- but not\nnecessarily the fluxes themselves --- annihilate each other. Our main result is\na rigorous proof of existence of weak solutions. The starting point is the\nformal representation of the dynamics as a constrained gradient flow in the\nWasserstein metric. We then show that time-discrete approximations by means of\nthe incremental minimizing movement scheme converge to a weak solution in the\nlimit. Further, we compare the non-local model to the classical Cahn-Hilliard\nmodel in numerical experiments. Our results illustrate the significant speed-up\nin the decay of the free energy due to the higher degree of freedom for the\nvelocity fields.\n