Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

Collection Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

Organizer(s) Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken

Date(s) 08/04/2019 - 12/04/2019

linked URL https://www.chairejeanmorlet.com/2104.html

00:00:00 / 00:00:00

21 22

The supercooled Stefan problem

By Mykhaylo Shkolnikov

We will 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 will 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. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal paper [Ste89] from 1889 for the ordinary Stefan problem. In our second main theorem, we will establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are present. Based on joint work with Francois Delarue and Sergey Nadtochiy.

Information about the video

Date of recording 12/04/2019
Date of publication 09/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19517903
Cite this video Shkolnikov, Mykhaylo (12/04/2019). The supercooled Stefan problem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19517903
URL https://dx.doi.org/10.24350/CIRM.V.19517903

Domain(s)

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2104/Slides/Shkolnikov.pdf

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