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Updated: Jun 22, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
Antonio Cordoba1, Diego Cordoba, Francisco Gancedo
1Department of Mathematics, Universidad Autonoma de Madrid, Carretera de Colmenar Viejo, Km. 15, 28049 Madrid, Spain.
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.
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