576 citations · 1.5k across the 43 of their papers we have counts for
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Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability
Rafael Granero-Belinchón, Steve Shkoller
We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is de…
Nonuniqueness of weak solutions to the SQG equation
Tristan Buckmaster, Steve Shkoller, Vlad Vicol
We prove that weak solutions of the inviscid SQG equations are not unique, thereby answering Open Problem 11 in the survey arXiv:1111.2700 by De Lellis and Székelyhidi Jr. Moreover…
Local well-posedness and Global stability of the Two-Phase Stefan problem
Mahir Hadzic, Gustavo Navarro, Steve Shkoller
The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solv…
A model for Rayleigh-Taylor mixing and interface turn-over
Rafael Granero-Belinchón, Steve Shkoller
We first develop a new mathematical model for two-fluid interface motion, subjected to the Rayleigh-Taylor (RT) instability in two-dimensional fluid flow, which in its simplest for…