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Splash singularity for water waves
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DOI：10.1073/pnas.1115948108.png)
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Abstract
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We exhibit smooth initial data for the two-dimensional (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.
Keywords:
blow-up
Euler
incompressible
free boundary
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