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The primitive equations on the large scale ocean under the small depth hypothesis. (English) Zbl 1048.35082
The authors establish the global existence of strong solutions of primitive equations for the large-scale ocean with small depth, which allows to introduce a small parameter (thickness parameter for a thin domain). The existence is proved for a large class of initial data and boundary conditions acting as external forcing. The proof is based on a detailed study of the dependence of a number of classical constants on the thickness of the domain, on a priori energy estimates, and on some functional inequalities.
MSC:
35Q35PDEs in connection with fluid mechanics
86A05Hydrology, hydrography, oceanography
35Q30Stokes and Navier-Stokes equations
76U05Rotating fluids