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Abstract:
We study the long time
existence of classical solutions to the Shallow
Water (SW) equations with pressure gradient and
rotational forcing that are both singular within
certain scaling regime of the Froude and Rossby
numbers. The SW dynamics is then shown to be
asymptotically close to the one governed by the 2-D
“pressureless” rotational Euler equations with
subcritical initial data, which in turn yields the
increasingly long time existence at this singular
regime. The novelty of our approach is the use of an
approximate system that is linear while still
capturing both the singularity and the advection
dynamics of the underlying nonlinear system. The
near periodic dynamics shown here is closely related
to the circular uid motions observed in geophysical
sciences.
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