Hamiltonian formalism for models of rotating shallow water insemigeostrophic scaling
Hamiltonian formalism for models of rotating shallow water insemigeostrophic scaling
复制标题
半地转尺度旋转浅水模型的哈密顿形式主义
DOI：
10.3934/dcds.2011.31.827
复制
发表时间：
2011
影响因子：
1.1
通讯作者：
S. Vasylkevych
中科院分区：
文献类型：
--
作者：
M. Oliver;S. Vasylkevych
本文首次提出了所谓的严谨研究
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 these models are Hamiltonian on the group of $H^s$
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 $H^s$ solutions locally in time.