Seminar 31/03/17: Geometric aspects of fluid models with vorticity

Geometric aspects of fluid models with vorticity
Tony Lyons
Waterford Institute of Technology
Friday 31 March 2017
4pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street


In this talk we outline a derivation of a two-component system of nonlinear PDE modelling shallow water-waves with vorticity. In line with several other well known shallow water models with quadratic nonlinearities, such as the Camassa-Holm and Hunter-Saxton equations, we show how this may be interpreted as a geodesic flow on an appropriate diffeomorphism group. We then outline how this geometric interpretation may be used to show the well-posedness of the fluid model, and establish criteria for the existence of global solutions for the system.