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arXiv · 2608.26842

Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow

Tim Laux·Keisuke Takasao
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Abstract

Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cahn equations. We prove - for the first time - a global, unconditional convergence result for such a coupled system and show that the limit is a multiphase mean curvature flow in the sense of Brakke.

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Tim Laux, Keisuke Takasao. 2026-08-27. Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow. https://arxiv.org/abs/2608.26842

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