Castro Martínez, ÁngelCórdoba Gazolaz, DiegoFefferman, Charles L.Gancedo García, FranciscoLópez Fernández, María2016-09-212016-09-212011-03-22Castro Martínez, Á., Córdoba Gazolaz, D., Fefferman, C.L., Gancedo García, F. y López Fernández, M. (2011). Turning waves and breakdown for incompressible flows. Proceedings of the National Academy of Sciences, 108 (12), 4754-4759.0027-84241091-6490http://hdl.handle.net/11441/45167We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (α, f0(α)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time ∗t where the solution of the free boundary problem parameterized as s (α, f(α, t)) blows up:: k∂αfkL∞(t∗) = ∞. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1073/pnas.1101518108