Stefan problem with surface tension: global existence of physical solutions under radial symmetry

Sergey Nadtochiy, Mykhaylo Shkolnikov

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Stefan problem with surface tension, also known as the Stefan–Gibbs–Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the initial data we introduce a novel “probabilistic” notion of solution, which can accommodate the discontinuities in time (of the radius) of the evolving aggregate. Our main result establishes the global existence of a probabilistic solution satisfying the natural upper bound on the sizes of the discontinuities. Moreover, we prove that the upper bound is sharp in dimensions d⩾ 3 , in the sense that none of the discontinuities in the solution can be decreased in magnitude. The detailed analysis of the discontinuities, via appropriate stochastic representations, differentiates this work from the previous literature on weak solutions to the Stefan problem with surface tension.

Original languageEnglish (US)
Pages (from-to)385-422
Number of pages38
JournalProbability Theory and Related Fields
Volume187
Issue number1-2
DOIs
StatePublished - Oct 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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