# Minimizing movements for mean curvature flow of partitions

## TL;DR

This paper establishes the existence and properties of a weak global mean curvature flow for space partitions using minimizing movements, extending to driven forces and connecting with classical solutions.

## Contribution

It introduces a new weak solution framework for mean curvature flow of partitions via minimizing movements, including stability and consistency results.

## Key findings

- Existence of weak global mean curvature flow for partitions.
- Extension to flows with driving forces.
- Consistency with classical and viscosity solutions.

## Abstract

We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.