Artículo
On the Muskat problem: global in time results in 2D and 3D
Autor/es | Constantin, Peter
Córdoba Gazolaz, Diego Gancedo García, Francisco Rodríguez Piazza, Luis Strain, Robert M. |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2016-12 |
Fecha de depósito | 2017-09-14 |
Publicado en |
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Resumen | This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong ... This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong and weak solutions with initial data controlled by explicit constants. Furthermore we refine the estimates from our paper [P. Constantin, D. Córdoba, F. Gancedo and R. M. Strain. On the global existence for the Muskat problem. J. Eur. Math. Soc. (JEMS) 15, 201-227 (2013)] to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2D. Finally we provide global in time results in critical spaces, giving solutions with bounded slope and time integrable bounded curvature. |
Agencias financiadoras | National Science Foundation (NSF). United States Ministerio de Ciencia e Innovación (MICIN). España |
Identificador del proyecto | DMS-1209394
DMS-1265132 MTM2011-26696 MTM2012-05622 DMS-1200747 DMS-0901463 info:eu-repo/grantAgreement/EC/FP7/203138 |
Cita | Constantin, P., Córdoba Gazolaz, D., Gancedo García, F., Rodríguez Piazza, L. y Strain, R.M. (2016). On the Muskat problem: global in time results in 2D and 3D. American Journal of Mathematics, 138 (6), 1455-1494. |
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