Two phase Stefan-type problem: Regularization near initial data by phase dynamics

TL;DR

This paper studies how solutions to the two-phase Stefan problem become smoother near initial data, introducing a new decomposition method to analyze regularity and generalize previous results.

Contribution

It presents a novel decomposition argument that extends prior techniques to two-phase problems, improving understanding of regularization near initial conditions.

Findings

Solutions are close to Lipschitz profiles at small scales.

The new method generalizes previous one-phase regularity results.

Enhanced understanding of phase dynamics near initial data.

Abstract

We investigate the regularizing behavior of two-phase Stefan problem near initial data. The main step in the analysis is to establish that in any given scale, the scaled solution is very close to a Lipschitz profile in space-time. We introduce a new decomposition argument to generalize the preceding ones by Choi, Jerion and Kim([CJK1], [CJK2]) and by Choi and Kim([CK]) on one-phase problems.