On the Muskat problem: global in time results in 2D and 3D
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. Further...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/64438 |
| Acceso en línea: | http://hdl.handle.net/11441/64438 https://doi.org/10.1353/ajm.2016.0044 |
| Access Level: | acceso abierto |
| Palabra clave: | Porous media Incompressible flows Fluid interface Global existence |
| Sumario: | 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. |
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