Splash singularity for water waves
Splash singularity for water waves
复制标题
水波的飞溅奇点
DOI：
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发表时间：
2011
影响因子：
11.1
通讯作者：
J. Gómez
中科院分区：
文献类型：
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作者：
A. Castro;D. Córdoba;C. Fefferman;F. Gancedo;J. Gómez
我们表现出光滑的初始数据的二维（2D）水波方程，我们证明了光滑的接口在有限时间内崩溃。此外，我们显示了一个稳定的结果与数值证据，存在的二维水波方程的解决方案，从一个图形开始，翻转，并在有限时间内崩溃的飞溅奇点（在一个点上的自相交曲线）。
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.