Weak-strong uniqueness for the mean curvature flow of double bubbles

TL;DR

This paper establishes a weak-strong uniqueness principle for BV solutions to three-dimensional multiphase mean curvature flow of triple line clusters, extending previous two-dimensional results using gradient-flow calibrations.

Contribution

It introduces a novel three-dimensional gradient-flow calibration for triple junction clusters, advancing the understanding of multiphase mean curvature flow.

Findings

Proves weak-strong uniqueness for BV solutions in 3D

Constructs explicit gradient-flow calibrations for triple junctions

Extends 2D techniques to 3D multiphase flows

Abstract

We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.