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A note on stability
shifting for the Muskat problem, II: From stable to unstable
and back to stable
Diego Córdoba, Javier Gómez-Serrano and Andrej Zlatoš |
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Vol. 10 (2017), No. 2, 367–378
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Abstract |
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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. (Philos. Trans. Roy. Soc. A 373:2050 (2015), art. id. 20140278). |
Keywords
Muskat problem, interface, incompressible fluid, porous
media, Rayleigh–Taylor, computer-assisted
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Mathematical Subject Classification 2010
Primary: 35Q35
Secondary: 35R35, 65G30, 76B03
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Supplementary materialAuxiliary tables and code for the proof of Lemmas 2.2.1 and 2.2.2 |
Milestones
Received: 27 January 2016
Revised: 26 October 2016
Accepted: 26 December 2016
Published: 23 February 2017
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Authors |
| Diego Córdoba | |
| Instituto de Ciencias
Matemáticas Consejo Superior de Investigaciones Científicas c/ Nicolas Cabrera 13-15 Campus Cantoblanco UAM 28049 Madrid Spain |
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| Javier Gómez-Serrano | |
| Department of Mathematics Princeton University 610 Fine Hall, Washington Rd Princeton, NJ 08544 United States |
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| Andrej Zlatoš | |
| Department of Mathematics University California San Diego 9500 Gilman Dr. #0112 La Jolla, CA 92093 United States |
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