  The aim of this paper is to prove that a three dimensional Lagrangian flow
which defines equatorially trapped water waves is dynamically possible. This is
achieved by applying a mixture of analytical and topological methods to prove
that the nonlinear exact solution to the geophysical governing equations,
derived by Constantin in J. Geophys. Res., 117 (2012), is a global
diffeomorphism from the Lagrangian labelling variables to the fluid domain
beneath the free surface.
