@article{cd3c649ea91643598f3f153d0f7296c2,
title = "A note on stability shifting for the Muskat problem, II: From 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 the existence of double stability shifting in the direction opposite to (as well as more difficult and more surprising than) the one shown by Cordoba et al.",
keywords = "Computer-assisted, Incompressible fluid, Interface, Muskat problem, Porous media, Rayleigh-Taylor",
author = "Diego C{\'o}rdoba and Javier G{\'o}mez-Serrano and Andrej Zlato{\v s}",
note = "Funding Information: C{\'o}rdoba and G{\'o}mez-Serrano were partially supported by the grant MTM2014-59488-P (Spain) and ICMAT Severo Ochoa project SEV-2011-0087. G{\'o}mez-Serrano was partially supported by an AMSSimons Travel Grant. Zlato{\v s} acknowledges partial support by NSF grants DMS-1652284 and DMS-1656269. We thank Princeton University for computing facilities (NewComp cluster). We are also very grateful to the anonymous referees for their valuable comments and suggestions. Publisher Copyright: {\textcopyright} 2017 Mathematical Sciences Publishers.",
year = "2017",
doi = "10.2140/apde.2017.10.367",
language = "English (US)",
volume = "10",
pages = "367--378",
journal = "Analysis and PDE",
issn = "2157-5045",
publisher = "Mathematical Sciences Publishers",
number = "2",
}