### Abstract

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e., the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.

Original language | English (US) |
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Article number | 115622 |

Journal | Journal of Mathematical Physics |

Volume | 53 |

Issue number | 11 |

DOIs | |

State | Published - Nov 27 2012 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Castro, A., Córdoba, D., Fefferman, C., Gancedo, F., & Gómez-Serrano, J. (2012). Finite time singularities for water waves with surface tension.

*Journal of Mathematical Physics*,*53*(11), [115622]. https://doi.org/10.1063/1.4765339