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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 " dimensional"
limit equations...
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