Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
arXiv:1102.1902
Abstract
The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.
38 pages, added new comments and a figure, corrected typos
References in corpus (6)
- On the global existence for the Muskat problem
- Breakdown of smoothness for the Muskat problem
- Absence of squirt singularities for the multi-phase Muskat problem
- Mathematics for 2d Interfaces
- A generalised Rayleigh-Taylor condition for the Muskat problem
- A stability criterion for two-fluid interfaces and applications