Abstract
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface selfintersects 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 twophase 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 blowup rates for the components of the velocity gradient which, in turn, allow us to characterize the geometry of the evolving interface just prior to selfintersection. The constraints on the geometry then lead to an impossible outcome, showing that our assumption of a finitetime splash singularity was false.
Original language  English 

Pages (fromto)  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)
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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)