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SUMMARY:Darren Crowdy (Imperial College London)
DTSTART:20221011T130000Z
DTEND:20221011T140000Z
DTSTAMP:20260422T201236Z
UID:CAvid/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/84/">W
 ater waves with vorticity and the Schwarz function</a>\nby Darren Crowdy (
 Imperial College London) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nThe theory of water waves is centurie
 s old\, but it remains a vibrant area of research. Most theoretical work o
 n water waves takes the flow to be irrotational\, but there has been growi
 ng interest\, especially recently\, in the effect of vorticity on the stru
 cture of the waves. The assumption of irrotationality has the theoretical 
 advantage that complex analysis techniques can be used to analyze the prob
 lem in the two-dimensional setting. This talk will present a novel theoret
 ical formulation of the problem of steadily-travelling water waves in the 
 presence of vorticity (where the assumption of irrotationality is dropped)
  but in the absence of gravity or capillarity. The approach is based on th
 e notion of a Schwarz function of a curve. It unifies our understanding of
  several recent results in the water wave literature and provides a wealth
  of new exact mathematical solutions to this challenging free boundary pro
 blem.\n
LOCATION:https://researchseminars.org/talk/CAvid/84/
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