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arXiv · 2611.04631

The Sharp Interface Limit of the Two-Dimensional Navier--Stokes/Allen--Cahn System as a Brakke Flow

Yuning Liu·Yoshihiro Tonegawa
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Abstract

We study the sharp-interface limit of the two-dimensional incompressible Navier--Stokes/Allen--Cahn system with constant mobility and prove the existence of global integral varifold solutions to the coupled Navier--Stokes/mean curvature flow system. The limiting interface measure satisfies Brakke's inequality, and its normal velocity equals the sum of its mean curvature and the normal projection of the fluid velocity.

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Yuning Liu, Yoshihiro Tonegawa. 2026-11-03. The Sharp Interface Limit of the Two-Dimensional Navier--Stokes/Allen--Cahn System as a Brakke Flow. https://arxiv.org/abs/2611.04631

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