Geodesic
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
Ángel Castro1 ; Diego Córdoba2 ; Charles Fefferman3 ; Francisco Gancedo4 ; María López-Fernández5
1 Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain
2 Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientíificas, 28049 Madrid, Spain
3 Department of Mathematics, Princeton University, Fine Hall - Washington Rd., Princeton, NJ 08544
4 Department of Mathematical Analysis, University of Seville, C/ Tarfia s/n, Campus Reina Mercedes, 41012 Sevilla, Spain
5 Institut für Mathematik, Universität Zürich, Zürich, Switzerland
Annals of mathematics, Tome 175 (2012) no. 2, pp. 909-948.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2012.175.2.9

Ángel Castro 1 ; Diego Córdoba 2 ; Charles Fefferman 3 ; Francisco Gancedo 4 ; María López-Fernández 5

1 Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain
2 Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientíificas, 28049 Madrid, Spain
3 Department of Mathematics, Princeton University, Fine Hall - Washington Rd., Princeton, NJ 08544
4 Department of Mathematical Analysis, University of Seville, C/ Tarfia s/n, Campus Reina Mercedes, 41012 Sevilla, Spain
5 Institut für Mathematik, Universität Zürich, Zürich, Switzerland 
@article{10_4007_annals_2012_175_2_9,
     author = {\'Angel Castro and Diego C\'ordoba and Charles Fefferman and Francisco Gancedo and Mar{\'\i}a L\'opez-Fern\'andez},
     title = {Rayleigh-Taylor breakdown for the {Muskat} problem with applications to water waves},
     journal = {Annals of mathematics},
     pages = {909--948},
     publisher = {mathdoc},
     volume = {175},
     number = {2},
     year = {2012},
     doi = {10.4007/annals.2012.175.2.9},
     mrnumber = {2993754},
     zbl = {06025004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.9/}
}
TY  - JOUR
AU  - Ángel Castro
AU  - Diego Córdoba
AU  - Charles Fefferman
AU  - Francisco Gancedo
AU  - María López-Fernández
TI  - Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
JO  - Annals of mathematics
PY  - 2012
SP  - 909
EP  - 948
VL  - 175
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.9/
DO  - 10.4007/annals.2012.175.2.9
LA  - en
ID  - 10_4007_annals_2012_175_2_9
ER  - 
%0 Journal Article
%A Ángel Castro
%A Diego Córdoba
%A Charles Fefferman
%A Francisco Gancedo
%A María López-Fernández
%T Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
%J Annals of mathematics
%D 2012
%P 909-948
%V 175
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.9/
%R 10.4007/annals.2012.175.2.9
%G en
%F 10_4007_annals_2012_175_2_9
Ángel Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; María López-Fernández. Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves. Annals of mathematics, Tome 175 (2012) no. 2, pp. 909-948. doi : 10.4007/annals.2012.175.2.9. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.9/

Cité par Sources :