## One-sided Mullins-Sekerka flow does not preserve convexity

### Summary

Summary: The Mullins-Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn-Hilliard equation. Assuming the existence of sufficiently smooth solutions we will show that the one-sided Mullins-Sekerka flow does not preserve convexity.

### Mathematics Subject Classification

35R35, 35J05, 35B50, 53A07

### Keywords/Phrases

Mullins-Sekerka flow, Hele-Shaw flow, Cahn-Hilliard equation, free boundary problem, convexity, curvature