Modulus of Continuity Method for the Muskat Problem and Fractional Mean Curvature Flow

Stephen Philip Cameron
In this work, we consider two nonlinear, nonlocal, parabolic equations and show that under appropriate growth assumptions, solutions regularize. The first is the 2d Muskat problem, which models the evolution of the interface between oil and water in a tar sand. In the stable regime, the equation was known to be well-posed for smooth, flat initial data, but the slope can blow up in finite time for some large initial data [CCF+12]. It was conjectured...
This data repository is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation.