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We establish, for smooth enough initial data, the global well-posedness(existence, uniqueness and continuous dependence on initial data) of solutions,for an inviscid three-dimensional {\it slow limiting ocean dynamics} model.This model was derived as a strong rotation limit of the rotating andstratified Boussinesg equations with periodic boundary conditions. To establishour results we utilize the tools developed for investigating thetwo-dimensional incompressible Euler equations and linear transport equations.Using a weaker formulation of the model we also show the global existence anduniqueness of solutions, for less regular initial data.

Global Regularity for an Inviscid Three-dimensional Slow Limiting Ocean Dynamics Model