Splash singularity for water waves.
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ABSTRACT:
SUBMITTER: Castro A
PROVIDER: S-EPMC3271900 | biostudies-other | 2012 Jan
REPOSITORIES: biostudies-other
Publications
Splash singularity for water waves.
Castro Angel A Córdoba Diego D Fefferman Charles L CL Gancedo Francisco F Gómez-Serrano Javier J
Proceedings of the National Academy of Sciences of the United States of America 20120104 3
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. ...[more]
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