Weak-strong uniqueness for the mean curvature flow of double bubbles (Q6040152)

The authors derive a weak-strong uniqueness for bounded variation solutions to multiphase mean curvature flow. The main contribution is to analyze a smoothly evolving regular double bubble admitting a family of transported weights on \([0,T]\). They restate the precise definition of the concept of a gradient flow calibration and verify its existence. Combining this result and the existence of a sufficiently regular and smoothly evolving double bubble in the three-dimensional setting with the conditional stability of any calibrated multiphase mean curvature flow in arbitrary dimensions they obtain the main result on the weak-strong uniqueness and the stability of evolutions.