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Artículo
Breakdown of smoothness for the Muskat problem
(Springer, 2013-06)
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 C4.
Artículo
Finite time singularities for the free boundary incompressible Euler equations
(Princeton University, 2013)
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the ...