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

2015/12/08 by Diego Córdoba, Javier Gómez-Serrano, Andrej Zlatoš · 1 citation
Mathematics · #math.AP

paper · pdf · doi:10.2140/apde.2017.10.367

published as Anal. PDE 10 (2017) 367-378 · 9 pages, plus 3 appendices of 15 pages, approx. 10.000 lines of code

arxiv created 2015/12/08 · arxiv updated 2017/03/08

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]

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• Existence, asymptotic behaviour and convergence of a generalised 3D Muskat problem in stable regime