The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces.
نویسندگان
چکیده
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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عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 106 27 شماره
صفحات -
تاریخ انتشار 2009