Seminar 22/2/19: Global diffeomorphism of the Lagrangian flow-map for Pollard-like solutions

Global diffeomorphism of the Lagrangian flow-map for Pollard-like solutions
Adrian Rodriguez Sanjurjo
University College Cork
Friday 22 February 2019
1pm, Blue Room, 4th floor, Main Building, TU Dublin, Kevin Street, City Campus

Abstract:

The aim of this talk is to provide a rigorous although accessible analysis of some nonlinear surface waves in the presence of a depth-invariant zonal current constituting a generalisation of Pollard's waves. These oceanic water waves, which are nonlinear solutions of the geophysical f-plane equations accounting for rotational effects, have an exact and explicit representation in the Lagrangian framework. This is indeed a remarkable discovery; however, in order to rigorously show their mathematical validity, the three-dimensional Lagrangian flow-map prescribing these solutions needs to be a global diffeomorphism. This constitutes the main result of the talk and it will be proven by applying a mixture of analytical and degree-theoretical arguments and by imposing certain conditions on the physical and Lagrangian labelling parameters.