Splash singularity for water waves.
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 109 3 شماره
صفحات -
تاریخ انتشار 2012