Mathematical Sciences: Geometric Structures

数学科学：几何结构

• 批准号: 9529369
• 负责人: Dennis Sullivan
• 金额: $ 15万
• 依托单位: CUNY Graduate School University Center
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9529369&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Structures

9529369 Sullivan This proposal seeks to lay a mathematical foundation for the continuum model of fluid motion in three dimensions. This relates to the investigator's earlier works on applying smooth manifold techniques to topological manifolds. The proposed research also deals with the newly discovered monopole equations of Seiberg and Witten: the proposal aims to determine exactly what structures the Seiberg-Witten invariants depend on. The fluid motion dynamics can be described by a system of nonlinear partial differential equations. There are traditional difficulties with the partial differential equation approach in that the system often is not smooth enough. The proposed research aims to introduce topological techniques not requiring any smoothness to these systems of equations.

9529369 Sullivan这个建议试图为三维流体运动的连续体模型奠定数学基础。这与研究者早期在将光滑流形技术应用于拓扑流形方面的工作有关。提议的研究也涉及到新发现的Seiberg和Witten的单极方程：提议的目的是确定Seiberg-Witten不变量所依赖的结构。流体运动动力学可以用非线性偏微分方程组来描述。传统的偏微分方程方法存在着系统不够光滑的困难。提出的研究旨在引入不需要任何平滑的拓扑技术到这些方程组。