New prior estimates for the solution to the system of equations of large-scale ocean are considered. These estimates supplement the results obtained by G.M. Kobelkov when proving the existence and uniqueness theorem and allow one to show the convergence of approximate solutions to the exact solution to the differential problem. Several new practical scheme are given. The results obtained in this paper supplement and develop the previous author's studies.

Keywords: nonlinear partial differential equations, ocean dynamics equations, primitive equations, Navier-Stokes equations, splitting methods, geophysical hydrodynamics

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