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Stability of traveling water waves with a point vortex

Presented by: 
Samuel Walsh University of Missouri
Date: 
Thursday 10th August 2017 - 09:00 to 10:00
Venue: 
INI Seminar Room 1
Abstract: 
In this talk, we will present recent results on the (conditional) orbital stabillity of two-dimensional steady capillary-gravity water waves with a point vortex. One can think of these waves as an idealization of traveling waves with compactly supported vorticity. The governing equations have a Hamiltonian formulation, and the waves themselves can be realized as minimizers of an energy subject to fixed momentum. We are able to deduce stability by using an abstract framework that generalizes the classical work of Grillakis, Shatah, and Strauss. In particular, our theory applies to systems where the sympletic operator is state dependent and may fail to be surjective. This is joint work with Kristoffer Varholm and Erik Wahlén 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons