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Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Anatoli Babin;  Alex Mahalov;  Basil Nicolaenko — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter ). This uniform existence is proven for periodic or stress-free boundary conditions for domain aspect ratios, including the case of three wave resonances which yield nonlinear " 2 1 2 dimensional" limit equations...

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