Work

Stefan Problem with Surface Tension: Uniqueness of Physical Solutions under Radial Symmetry

Year: 2024

Type: article

Abstract: We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently introduced in [21]. The paper in hand is devoted to the proof that the physical solution is unique, the first such result when the free boundary is not flat, or when two phases are present. The main argument relies on a detailed analysis of the hitting probabilities for a three-dimensional Brownian motion, as well as on a novel convexity property of the free boundary obtained by comparison techniques. In the course of the proof, we establish a wide variety of regularity estimates for the free boundary and for the temperature function, of interest in their own right.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-024-02026-3

Authors: Yucheng Guo, Sergey Nadtochiy, Mykhaylo Shkolnikov

Institutions: Princeton University, Illinois Institute of Technology, Carnegie Mellon University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funders: National Science Foundation, Carnegie Mellon University, Division of Mathematical Sciences