Splash singularity for water waves

Details Splash singularity for water waves Splash singularity for water waves

2011-06-10

arxiv.org/abs/1106.2120v2

Mathematics

Analysis of PDEs

19 pages, 4 figures

Scientific paper

We exhibit smooth initial data for the 2D water wave equation for which we prove that smoothness of the interface breaks down in finite time. 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.

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