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

TL;DR

This paper demonstrates the existence of solutions to the Muskat problem that transition from stable to unstable and back to stable, revealing complex stability dynamics in fluid interface evolution.

Contribution

It proves the existence of solutions exhibiting double stability shifts in the Muskat problem, extending previous results on stability transitions.

Findings

Solutions can shift stability twice in the Muskat problem.

Stability transitions can occur in the opposite direction to prior findings.

The results confirm complex stability behavior in fluid interface models.

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 [C\'ordoba, G\'omez-Serrano, Zlato\v{s}, A note on stability shifting for the Muskat problem. Phil. Trans. Roy. Soc. A, 373 (20140278), 2015]