A note on stability shifting for the Muskat problem

Abstract

In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable, and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized $L^{\infty }$ norm of the derivative of the initial condition that develop a turning singularity.

12 pages, 4 figures

References in corpus (1)

• A maximum principle for the Muskat problem for fluids with different densities

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• Entropy solutions to macroscopic IPM