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SUMMARY:Steady water waves with vorticity
DTSTART:20240517T141500
DTSTAMP:20260508T135727Z
UID:d50644fbd48bbbdb665b71598e4ca3ef884b6c86c4965b47b5c35c8f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Erik Wahlén\n\nLund University - Sweden\nAbstract:\nThe
  steady water wave problem is a classical topic in fluid mechanics which h
 as been studied for over two centuries. It concerns the steady flow of an 
 ideal fluid subject to gravity\, bounded above by a free surface. Mathemat
 ically it boils down to an elliptic free boundary problem for the stream f
 unction. The most well-known situation is that of irrotational flow\, wher
 e the PDE is simply Laplace’s equation with both Dirichlet and Neumann c
 onditions at the free surface. In that case\, Stokes conjectured the exist
 ence of a highest wave with a peaked crest\, which was verified a century 
 later in a seminal work by Amick\, Fraenkel and Toland. If one includes vo
 rticity\, Laplace’s equation changes to a semilinear elliptic equation. 
 This has some dramatic effects which are not yet completely understood. In
  particular\, it opens the door to overhanging waves and `cat’s eye’ v
 ortices. In my talk\, I will report on recent progress on these phenomena\
 , including a new formulation of the problem which allows for overhanging 
 waves and has a structure which is suitable for global bifurcation theory.
 \nBased on joint work with Jörg Weber (University of Vienna).
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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