On the existence of canonical multi-phase Brakke flows

This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is Brakke flow and BV solution at same time. In particular, we prove validity explicit identity concerning change volume grains, showing that their boundaries move according to generalized vector flow. As consequence results recently established by Fischer et al. in arXiv:2003.05478, under suitable assumptions on such additional property resolves non-uniqueness issue flows.