A Center Manifold Analysis for the Mullins–Sekerka Model

The Mullins–Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn–Hilliard equation. We show that classical solutions exist globally and tend to spheres exponentially fast, provided that they are close to a sphere initially. Our analysis is based on center manifold theory and on maximal regularity.