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Abstract
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We consider the water wave problem -- the free boundary problem of the Euler equation -- and construct small traveling wave solutions with vorticity based on a bifurcation method. Unlike those perturbed from shear flows, the vorticity of these solutions are supported in a small domain away from the water surface. We also discuss the global bifurcation of such waves when the vorticity is a delta mess. This is a joint work with Jalal Shatah and Sam Walsh.
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