Artículo
Turning waves and breakdown for incompressible flows
Autor/es | Castro Martínez, Ángel
Córdoba Gazolaz, Diego Fefferman, Charles L. Gancedo García, Francisco López Fernández, María |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2011-03-22 |
Fecha de depósito | 2016-09-21 |
Publicado en |
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Resumen | We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial ... We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (α, f0(α)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time ∗t where the solution of the free boundary problem parameterized as s (α, f(α, t)) blows up:: k∂αfkL∞(t∗) = ∞. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down. |
Identificador del proyecto | MTM2008-03754
info:eu-repo/grantAgreement/EC/FP7/203138 DMS-0901040 ONR00014-08-1-0678 DMS-0901810 MTM2008-03541 MTM2010-19510 |
Cita | Castro Martínez, Á., Córdoba Gazolaz, D., Fefferman, C.L., Gancedo García, F. y López Fernández, M. (2011). Turning waves and breakdown for incompressible flows. Proceedings of the National Academy of Sciences, 108 (12), 4754-4759. |
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