title: The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces.
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.
authors: Department of Mathematics, Universidad Autonoma de Madrid, Carretera de Colmenar Viejo, Km. 15, 28049 Madrid, Spain.
authors: Antonio
authors: A
authors: Cordoba
authors: Diego
authors: D
authors: Cordoba
authors: Francisco
authors: F
authors: Gancedo