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arXiv · 1501.02694

A note on stability shifting for the Muskat problem

Diego Córdoba·Javier Gómez-Serrano·Andrej Zlatoš
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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.

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Diego Córdoba, Javier Gómez-Serrano, Andrej Zlatoš. 2015-02-06. A note on stability shifting for the Muskat problem. https://doi.org/10.1098/rsta.2014.0278

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