A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable

Abstract

In this note, we show that there exist solutions of the Muskat problem which shift stability regimes in the following sense: they start stable, then become unstable, and finally return back to the stable regime. This proves existence of double stability shifting in the direction opposite to the one shown in [Córdoba, Gómez-Serrano, Zlatoš, A note on stability shifting for the Muskat problem. Phil. Trans. Roy. Soc. A, 373 (20140278), 2015]

9 pages, plus 3 appendices of 15 pages, approx. 10.000 lines of code

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