Spitalfields 2: Steve Shkoller speaks on singularities of overhanging and pre-breaking waves

antarcticSteve Shkoller spoke about dynamic interface singularities in the Euler equations.  He started by reviewing previous work on the “splash singularity”, showing how the result of Coutand & Shkoller (2014) extends to 3D, using different methods, a proof of Castro, Cordoba, Fefferman, Gancedo, Gomez-Serrano (2012). The main part of the talk was devoted to the case where there are two fluids.  He started by summarizing the recent result of Fefferman, Ionescu & Lie (2013) which proved that splash singularities could not occur in this case.  Then Steve presented a new proof of this result using different methods.  The principal tool was to derive an ODE for the tangential derivative of the tangential component of the velocity difference.  This ODE could then be analyzed exactly.  A preprint on this work can be found here. The talk also included a range of videos of large breaking waves, an example is the Teahupoo video.  A video of the talk is available here.

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