We will discuss the supercooled Stefan problem, which is a classical model describing the freezing of supercooled water (namely the unstable state of water below freezing temperature). I will introduce the PDE formulation of the problem introduced by Stefan, with some literature that exhibits instability of solutions. I will then describe the variational approach for the problem, which is motivated by the underlying interacting particle systems. As a consequence of our approach we will in particular obtain a global-time existence of solutions in general geometry.
The results I will discuss includes joint work with Young-Heon Kim (UBC) and with Sunhi Choi (Arizona).