Breakdown of smoothness for the Muskat problem

Details Breakdown of smoothness for the Muskat problem Breakdown of smoothness for the Muskat problem

2012-01-12

arxiv.org/abs/1201.2525v2

Mathematics

Analysis of PDEs

93 pages, 10 figures (6 added)

Scientific paper

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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