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M. Oliver and S. Vasylkevych,
Hamiltonian formalism for models of rotating shallow water in
semigeostrophic scaling,
Discret. Contin. Dyn. S. 31 (2011), 827-846.
Abstract:
This paper presents a first rigorous study of the so-called
large-scale semigeostrophic equations which were first introduced by
R. Salmon in 1985 and later generalized by the first author. We show
that the generalized equations are Hamiltonian on the group
of Hs diffeomorphisms for s>2. Notably,
in the Hamiltonian setting an apparent topological restriction on the
Coriolis parameter disappears. We then derive the corresponding
Hamiltonian formulation in Eulerian variables via Poisson reduction
and give a simple argument for the existence of Hs
solutions locally in time.
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