A note on stability shifting for the Muskat problem, II: From stable to unstable and back to stable

Diego Córdoba; Javier Gómez-Serrano; Andrej Zlatoš

doi:10.2140/apde.2017.10.367

A note on stability shifting for the Muskat problem, II: From stable to unstable and back to stable

Diego Córdoba, Javier Gómez-Serrano, Andrej Zlatoš

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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.

Original language	English (US)
Pages (from-to)	367-378
Number of pages	12
Journal	Analysis and PDE
Volume	10
Issue number	2
DOIs	https://doi.org/10.2140/apde.2017.10.367
State	Published - 2017

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Applied Mathematics

Keywords

Computer-assisted
Incompressible fluid
Interface
Muskat problem
Porous media
Rayleigh-Taylor

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10.2140/apde.2017.10.367

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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.",

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AU - Zlatoš, Andrej

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AB - 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.

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KW - Interface

KW - Muskat problem

KW - Porous media

KW - Rayleigh-Taylor

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A note on stability shifting for the Muskat problem, II: From stable to unstable and back to stable

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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