On the existence of canonical multi-phase free boundary Brakke flows: a case study

We establish the global-in-time existence of a codimension $1$ canonical multi-phase free boundary Brakke flow in the upper halfspace which is integer rectifiable up boundary, starting from a countably $n$-rectifiable set. Under a suitable uniform density ratio assumption on the initial datum, we show that the free boundary carries no positive mass for some short time.