Sharp Convergence to the Half-Space for Mullins-Sekerka in the Plane
Analysis of PDEs
2026-03-10 v2
Abstract
We revisit the HED Method for the Mullins-Sekerka evolution in the plane. We identify a natural notion of distance, intrinsic to the interface itself. Using this distance, the energy, and the dissipation, we develop natural assumptions on the flow and, assuming existence of a solution satisfying these conditions, establish not just the algebraic rate (previously derived by Chugreeva, Otto, and M. G. Westdickenberg) but also the sharp leading order constant for the convergence to the flat limiting interface.
Cite
@article{arxiv.2511.23270,
title = {Sharp Convergence to the Half-Space for Mullins-Sekerka in the Plane},
author = {Wenhui Shi and Maria G. Westdickenberg and Michael Westdickenberg},
journal= {arXiv preprint arXiv:2511.23270},
year = {2026}
}