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The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces

 

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Opened Access The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
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Author: Córdoba Barba, Antonio
Córdoba Gazolaz, Diego
Gancedo García, Francisco
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2009-07-07
Published in: Proceedings of the National Academy of Sciences, 106 (27), 10955-10959.
Document type: Article
Abstract: For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different because it emphasizes the active scalar character of the system and does not require the presence of gravity.
Cite: Córdoba Barba, A., Córdoba Gazolaz, D. y Gancedo García, F. (2009). The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces. Proceedings of the National Academy of Sciences, 106 (27), 10955-10959.
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URI: http://hdl.handle.net/11441/45168

DOI: 10.1073/pnas.0809874106

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