Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness

Understand

We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension.

• A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the freezing rate.
• We provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process.
• The latter is shown to transition between (i) continuous differentiability, (ii) Holder continuity, and (iii) discontinuity.