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

Antonio Cordóba | Zendy; Diego Córdoba | Zendy; Francisco Gancedo | Zendy

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

Author(s) -

Antonio Cordóba,

Diego Córdoba,

Francisco Gancedo

Publication year - 2009

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.0809874106

Subject(s) - conservative vector field , compressibility , infinity , rayleigh scattering , mathematical analysis , boundary value problem , physics , scalar (mathematics) , euler's formula , mathematics , mechanics , classical mechanics , geometry , optics

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.

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