### Abstract

In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for d-dimensional flows, or 3, the free-surface of a viscous water wave, modeled by the incompressible Navier–Stokes equations with moving free-boundary, has a finite-time splash singularity for a large class of specially prepared initial data. In particular, we prove that given a sufficiently smooth initial boundary (which is close to self-intersection) and a divergence-free velocity field designed to push the boundary towards self-intersection, the interface will indeed self-intersect in finite time.

Original language | English |
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Journal | Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire |

Early online date | 17 Jul 2018 |

DOIs | |

Publication status | E-pub ahead of print - 17 Jul 2018 |

### Keywords

- Navier–Stokes
- Free-boundary problem
- Finite-time singularity
- Splash singularity
- Interface singularity

### ASJC Scopus subject areas

- Mathematics(all)

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## Profiles

## Daniel Coutand

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

Person: Academic (Research & Teaching)