Analysis Seminar

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Solitary Water Waves on Shear Flows and with Surface Pressure

Speaker: Miles Wheeler, Courant

Location: Warren Weaver Hall 1302

Date: Thursday, September 25, 2014, 11 a.m.

Synopsis:

In this talk we will consider steady traveling solitary water waves which have "large amplitude" in the sense that they are not well-described by traveling wave solutions of KdV. After proving lower and upper bounds on the wave speed and some qualitative properties of the surface profile, we will construct exact solutions using a degree-theoretic continuation argument. Here the novelty will be in the inclusion of an arbitrary distribution of vorticity in the mean flow and/or a prescribed non-constant pressure on the surface.