Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves

Ángel Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; María López-Fernández

doi:10.4007/annals.2012.175.2.9

Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves

Ángel Castro
, Diego Córdoba
, Charles Fefferman
, Francisco Gancedo
, María López-Fernández

Mathematics

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

122 Scopus citations

Abstract

The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.

Original language	English (US)
Pages (from-to)	909-948
Number of pages	40
Journal	Annals of Mathematics
Volume	175
Issue number	2
DOIs	https://doi.org/10.4007/annals.2012.175.2.9
State	Published - Mar 2012

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.4007/annals.2012.175.2.9

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title = "Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves",

abstract = "The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.",

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AU - Castro, Ángel

AU - Córdoba, Diego

AU - Fefferman, Charles

AU - Gancedo, Francisco

AU - López-Fernández, María

PY - 2012/3

Y1 - 2012/3

N2 - The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.

AB - The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.

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EP - 948

JO - Annals of Mathematics

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Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves

Abstract

All Science Journal Classification (ASJC) codes

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