5 papers
Singularity formation and self-shrinkers for the parabolic Bernoulli problem
Hunter Liu, Sebastian Munoz, Zihui Zhao
We study singularity formation for classical solutions of the parabolic Bernoulli free boundary problem and the associated self-similar profiles. Inspired by Ricci and mean curvatu…
Space-time geometry of Hele-Shaw flow
Carson Collins, Inwon Kim, Sebastian Munoz
We study the dynamic behavior of the free boundary of the Hele-Shaw flow with a nonnegative source, in which the pressure satisfies in and the free boundary moves…
The supercooled Stefan problem: fractal freezing and the fine structure of maximal solutions
Raymond Chu, Inwon Kim, Sebastian Munoz
We study the supercooled Stefan problem in arbitrary dimensions. First, we study general solutions and their irregularities, showing generic fractal freezing and nucleation, based…
Regularity of the free boundary for the supercooled Stefan problem in arbitrary dimensions
Max Engelstein, Inwon Kim, Sebastian Munoz
We study the free boundary in the supercooled Stefan problem, a classical model for the solidification of water below its freezing temperature. In contrast with the melting problem…
Free boundary regularity and well-posedness of physical solutions to the supercooled Stefan problem
Sebastian Munoz
We study the regularity and well-posedness of physical solutions to the supercooled Stefan problem. Assuming only that the initial temperature is integrable, we prove that the free…