发表机构
University of Toronto; Chalmers University of Technology and University of Gothenburg; West University of Timişoara（多伦多大学; 查尔姆斯理工大学和哥德堡大学; 蒂米什瓦拉西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在奇异1-形式密度上定义辛结构，在增广三元组上定义预辛结构，作为可压缩流体中Marsden-Weinstein辛结构的模拟，并阐明其介于Weinstein与Marsden-Weinstein两种设置之间的中间地位。
AI 中文摘要
我们在奇异 1-形式密度上定义了辛结构，并在增广三元组上定义了预辛结构，这是不可压缩情形下涡旋膜上 Marsden-Weinstein 辛结构的可压缩模拟。增广三元组的等价类可视为可压缩流体中的特殊涡度，即流形全微分同胚群李代数对偶中的奇异元素，而 Marsden-Weinstein 辛结构与体积保持微分同胚群的奇异涡度相关。奇异 1-形式密度上的这种结构介于另外两种设置之间，我们重新审视了这两种设置：辛流形上加权各向同性子流形的 Weinstein 辛结构，以及涡旋膜上的 Marsden-Weinstein 辛结构。
英文摘要
We define a symplectic structure on singular 1-form densities and a presymplectic structure on augmented triples, a compressible analog of the Marsden--Weinstein symplectic structure on vortex membranes in the incompressible case. Equivalence classes of augmented triples can be regarded as special vorticities in compressible fluids, i.e., singular elements of the dual to the Lie algebra of the group of all diffeomorphisms of a manifold, while Marsden--Weinstein symplectic structure is related to singular vorticities for the group of volume-preserving diffeomorphisms. This structure on singular 1-form densities occupies an intermediate position between two other settings, which we revisit, the Weinstein symplectic structure on weighted isotropic submanifolds of symplectic manifolds and the Marsden--Weinstein symplectic structure on vortex membranes.
Comments19 pages, 1 figure
