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arXiv · 1106.2120

Splash singularity for water waves

Angel Castro·Diego Córdoba·Charles Fefferman·Francisco Gancedo·Javier Gómez-Serrano
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Abstract

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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Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier Gómez-Serrano. 2011-06-10. Splash singularity for water waves. https://doi.org/10.1073/pnas.1115948108

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