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SUMMARY:Global Bifurcation of Steady Gravity Water Waves with Critical Lay
 ers - Varvaruca\, E (University of Reading)
DTSTART:20140527T101500Z
DTEND:20140527T111000Z
UID:TALK52791@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:I will present some recent results on the problem of two-dimen
 sional travelling water waves propagating under the influence of gravity i
 n a flow of constant vorticity over a flat bed. By means of a conformal ma
 pping and an application of Riemann-Hilbert theory\, the free-boundary pro
 blem is equivalently reformulated as a one-dimensional pseudodifferential 
 equation which involves a modified Hilbert transform and\, moreover\, has 
 a variational structure. Using the new formulation\, existence is establis
 hed\, by means of real-analytic global bifurcation theory\, of a family of
  solutions which includes waves of large amplitude\, even in the presence 
 of critical layers in the flow. This is joint work with Adrian Constantin 
 and Walter Strauss.\n
LOCATION:Seminar Room 1\, Newton Institute
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