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Updated: Jun 22, 2026
06:42
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.
Summary
This study proves local-in-time existence for free boundary dynamics in Hele-Shaw, Muskat problems, and water waves under initial Rayleigh-Taylor stability. The novel approach highlights the active scalar nature without needing gravity.
Area of Science:
- Fluid dynamics
- Mathematical physics
Background:
- Free boundary problems like Hele-Shaw and Muskat are crucial in fluid dynamics.
- The irrotational incompressible Euler equation governs inviscid fluid flow.
- Rayleigh-Taylor instability is a key phenomenon at fluid interfaces.
Purpose of the Study:
- To establish local-in-time existence for 2D interface dynamics in Hele-Shaw, Muskat, and water wave problems.
- To present a novel approach for analyzing these systems.
- To demonstrate the applicability of the active scalar method.
Main Methods:
- Utilizing an active scalar formulation of the fluid dynamics equations.
- Focusing on the 2D interface dynamics.
- Applying mathematical analysis to prove local existence.
Main Results:
- Local-in-time existence is proven for the specified free boundary problems when the Rayleigh-Taylor condition is initially satisfied.
- The approach is distinct from prior work on water waves, notably not requiring gravity.
- The active scalar character of the system is emphasized.
Conclusions:
- The active scalar method provides a viable framework for studying complex fluid interfaces.
- The findings extend the understanding of stability and existence in free boundary fluid dynamics.
- This work offers a new perspective on the irrotational incompressible Euler equation.
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