1201.2525 (Angel Castro et al.)

Breakdown of smoothness for the Muskat problem    [PDF]

Angel Castro, Diego Cordoba, Charles Fefferman, Francisco Gancedo

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 $C^4$.

View original: http://arxiv.org/abs/1201.2525