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Finite time singularities for the free boundary incompressible Euler equations

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Topological Dynamics in the Physical and Biological Sciences

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 interface breaks down in finite time into a splash singularity or a splat singularity. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water wave equation that start from a graph, turn over and collapse in a splash singularity (self intersecting curve in one point) in finite time. Joint work with A. Castro, C. Fefferman, F. Gancedo and J. Gomez-Serrano.

This talk is part of the Isaac Newton Institute Seminar Series series.

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