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Outline

Organizers :

Y.Giga (University of Tokyo/Hokkaido University)

Period :

June 13, 2007 (Wednesday) 10:30-11:30

Place :

Graduate School of Mathematical Sciences the University of Tokyo, Room #056

Programme :

Professor Walter Strauss (Brown University)

TITLE:

Steady Water Waves with Vorticity

ABSTRACT:

Consider a classical 2D water wave under the influence of gravity with an arbitrary vorticity function. Assume such a wave is traveling at a constant speed over a flat bed. Then there exist many families of such waves of large amplitude. The proof is based on elliptic PDEs, bifurcation and degree theory. I will also exhibit some recent numerical computations. If the vorticity is sufficiently large, the first stagnation point occurs not at the crest (as with irrotational flows) but on the bed directly below the crest. For variable vorticity the first stagnation point can occur in the interior of the fluid.