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On the Muskat problem: global in time results in 2D and 3D

Opened Access On the Muskat problem: global in time results in 2D and 3D

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Autor: Constantin, Peter
Córdoba Gazolaz, Diego
Gancedo García, Francisco
Rodríguez Piazza, Luis
Strain, Robert M.
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2016-12
Publicado en: American Journal of Mathematics, 138 (6), 1455-1494.
Tipo de documento: Artículo
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 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.
Tamaño: 367.9Kb
Formato: PDF

URI: http://hdl.handle.net/11441/64438

DOI: 10.1353/ajm.2016.0044

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