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Global regularity for an inviscid three-dimensional slow limiting ocean dynamics model. (English) Zbl 1305.35107

Summary: 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 slow limiting ocean dynamics model. This model was derived as a strong rotation limit of the rotating and stratified Boussinesq equations with periodic boundary conditions. To establish our results, we utilize the tools developed for investigating the two-dimensional incompressible Euler equations and linear transport equations. Using a weaker formulation of the model, we also show the global existence and uniqueness of solutions, for less regular initial data.

MSC:

35Q31 Euler equations
86A10 Meteorology and atmospheric physics
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology

Biographic References:

Slemrod, Marshall
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