Consistency for the surface diffusion flat flow in three dimensions

2025/02/19 by Marco Cicalese, Cicalese, Marco, Nicola Fusco +5 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films

paper · pdf · doi:10.48550/arxiv.2502.13556

openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the flat flow solution for the surface diffusion equation via the discrete minimizing movements scheme proposed by Cahn and Taylor. We prove that in dimension three the scheme converges to the unique smooth solution of the equation, provided that the initial set is sufficiently regular.

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