### Abstract

In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. By means of elementary arguments, we prove that such a singularity cannot occur in finite time for vortex sheet evolution, that is for the two-phase incompressible Euler equations. We prove this by contradiction; we assume that a splash singularity does indeed occur in finite time. Based on this assumption, we find precise blow-up rates for the components of the velocity gradient which, in turn, allow us to characterize the geometry of the evolving interface just prior to self-intersection. The constraints on the geometry then lead to an impossible outcome, showing that our assumption of a finite-time splash singularity was false.

Original language | English |
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Pages (from-to) | 987–1033 |

Number of pages | 47 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 221 |

Issue number | 2 |

Early online date | 24 Feb 2016 |

DOIs | |

Publication status | Published - Aug 2016 |

### ASJC Scopus subject areas

- Analysis
- Mechanical Engineering
- Mathematics (miscellaneous)

## Fingerprint Dive into the research topics of 'On the Impossibility of Finite-Time Splash Singularities for Vortex Sheets'. Together they form a unique fingerprint.

## Profiles

## Daniel Coutand

- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Mathematics - Associate Professor

Person: Academic (Research & Teaching)

## Cite this

*Archive for Rational Mechanics and Analysis*,

*221*(2), 987–1033. https://doi.org/10.1007/s00205-016-0977-z