Spitalfields 3: Eugen Varvaruca speaks on singularities of steady flows

Stokes-maxEugen Varvaruca spoke on singularities of steady free surface flows.  He starting by reviewing the history of the classic case of the largest periodic Stokes wave from Stokes conjecture to the proof of Amick, Fraenkel & Toland (1982).  Then he reviewed the generalisation of this conjecture to include vorticity which culminated in Varvaruca (2009).  The main part of the talk was on three-dimensional axisymmetric gravity waves without swirl.  Stagnation points as well as points on the axis of symmetry were analyzed. The latter can have downward-pointing cusps.  At stagnation points on the axis of symmetry the unique blowup profile found was the Garabedian pointed bubble.  An asymptotic form of the velocity field is found.  Concentration compactness is used.  A recent paper on this is Varvaruca & Weiss (2014). A video of the talk is available here.

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