Poisson几何与地转方程的首次积分
Poisson geometry and first integrals of geostrophic equations
摘要：
我们描述了地转方程的首次积分，它类似于理想不可压缩流体的欧拉方程的拟能不变量。我们解释了这种相似性背后的几何，给出了几个等价的定义的泊松结构的空间上的光滑密度的辛流形，并显示它如何可以通过从一个辛结构的哈密顿约化的同构群。
英文摘要：
We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions of the Poisson structure on the space of smooth densities on a symplectic manifold, and show how it can be obtained via the Hamiltonian reduction from a symplectic structure on the diffeomorphism group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
