Breakdown of smoothness for the Muskat problem
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Abstract
In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down i.e. no longer belongs to $C^4$.
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This publication has 11 references indexed in Scilit:
- On the global existence for the Muskat problemJournal of the European Mathematical Society, 2012
- Rayleigh-Taylor breakdown for the Muskat problem with applications to water wavesAnnals of Mathematics, 2012
- Convex integration for a class of active scalar equationsJournal of the American Mathematical Society, 2011
- Turning waves and breakdown for incompressible flowsProceedings of the National Academy of Sciences, 2011
- Lack of Uniqueness for Weak Solutions of the Incompressible Porous Media EquationArchive for Rational Mechanics and Analysis, 2010
- Contour Dynamics of Incompressible 3-D Fluids in a Porous Medium with Different DensitiesCommunications in Mathematical Physics, 2007
- Global existence, singular solutions, and ill‐posedness for the Muskat problemCommunications on Pure and Applied Mathematics, 2004
- A pointwise estimate for fractionary derivatives with applications to partial differential equationsProceedings of the National Academy of Sciences, 2003
- Global solutions for small data to the Hele-Shaw problemNonlinearity, 1993
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquidProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1958