Loss of embeddedness for the one-phase quasistationary Stefan problem in 2D

TL;DR

This paper demonstrates that a smooth, embedded initial state in a 2D quasistationary Stefan problem can lose embeddedness in finite time, highlighting complex geometric evolution in phase change models.

Contribution

It provides the first example of finite-time loss of embeddedness for smooth initial data in this specific phase transition problem.

Findings

Embeddedness can be lost in finite time in 2D Stefan problems.

Smooth initial states do not guarantee preservation of embeddedness.

The example involves Gibbs-Thomson correction and kinetic undercooling.

Abstract

We provide an example for a smooth and embedded initial state that looses embeddedness in finite time when evolving according to the quasistationary Stefan problem with Gibbs-Thomson correction and kinetic undercooling in 2D.