论文标题
几何流体动力学和无限维牛顿方程
Geometric hydrodynamics and infinite-dimensional Newton's equations
论文作者
论文摘要
我们重新审视理想流体动力学的大地测量方法，并在牛顿方程式上为差异和概率密度的空间提供了相关的几何框架。后一个设置足以包括可压缩和不可压缩的流体动力学，磁性流体动力学，浅水系统和相对论流体方程的方程。我们使用无限维信息几何形状，最佳运输，Madelung变换以及Simphectic和Poisson减少的形式主义的工具，通过对选定示例以及新结果进行调查来说明这一点。
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include equations of compressible and incompressible fluid dynamics, magnetohydrodynamics, shallow water systems and equations of relativistic fluids. We illustrate this with a survey of selected examples, as well as with new results, using the tools of infinite-dimensional information geometry, optimal transport, the Madelung transform, and the formalism of symplectic and Poisson reduction.
