The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
Open Access
- 7 July 2009
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 106 (27) , 10955-10959
- https://doi.org/10.1073/pnas.0809874106
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.Keywords
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