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Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves. (English) Zbl 1267.76033

The Muskat problem models the evolution of interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. Here, the authors show that the Rayleigh-Taylor condition may hold initially, but break down in finite time. As a consequence, the authors prove the existence of turning of water waves.

MSC:

76E17 Interfacial stability and instability in hydrodynamic stability
76S05 Flows in porous media; filtration; seepage
76D33 Waves for incompressible viscous fluids
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