Abstract
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface selfintersects in finite time. We prove that for ddimensional flows, or 3, the freesurface of a viscous water wave, modeled by the incompressible Navier–Stokes equations with moving freeboundary, has a finitetime 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 selfintersection) and a divergencefree velocity field designed to push the boundary towards selfintersection, the interface will indeed selfintersect in finite time.
Original language  English 

Pages (fromto)  475503 
Number of pages  29 
Journal  Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 
Volume  36 
Issue number  2 
Early online date  17 Jul 2018 
DOIs  
Publication status  Epub ahead of print  17 Jul 2018 
Keywords
 Navier–Stokes
 Freeboundary problem
 Finitetime 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)