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

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-03
DOI
https://doi.org/10.48550/arxiv.2611.04631
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

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

Yoshihiro Tonegawa, Yuning Liu
arXiv (Cornell University)
Geometric Analysis and Curvature Flows
preprint

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

Yoshihiro Tonegawa, Yuning Liu
preprint en

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.

arXiv (Cornell University)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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The Sharp Interface Limit of the Two-Dimensional Navier--Stokes/Allen--Cahn System as a Brakke Flow — Yoshihiro Tonegawa, Yuning Liu · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS