TY - JOUR
T1 - Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
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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U2 - 10.4007/annals.2012.175.2.9
DO - 10.4007/annals.2012.175.2.9
M3 - Article
AN - SCOPUS:84857721683
SN - 0003-486X
VL - 175
SP - 909
EP - 948
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 2
ER -