Weak Singularities and Transport for Incompressible Flows of an Ideal Fluid

理想流体不可压缩流动的弱奇异性和输运

• 批准号: 9876947
• 负责人: Mikhail Vishik
• 金额: $ 8.91万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9876947&HistoricalAwards=false
• 关键词: Weak; Singularities; Transport; Incompressible; Flows

9876947VishikThe principal investigator will study the mathematical problems of fluid motion. Methods of Littlewood-Paley theory and wavelets will be used to study weak singularities for the incompressible flows of an ideal fluid. The basic nonstationary problem for the Euler equations will be investigated in function classes with, generally, essentially unbounded vorticity. He will address the problem of linear vector transport by flows that are less than regular. These aspects of transport theory are directly applicable to questions of existence and uniqueness for the Euler equations.The mathematical theory of fluid motion is fundamental both for applications in meteorology, geophysics, astrophysics and within mathematics itself. Most of the flows in nature such as ocean currents, or hurricanes, or the motion of matter in a galaxy, are highly irregular. The origin and evolution of singular structures such as rapid oscillations of a flow are still not well understood. In addition to this, numerical modelling of irregular flows is limited by instabilities due to the small scale structures constantly produced by the flow. The PI will investigate two related aspects of this subject. First, the basic mathematical nature of the flows with singularities. Second, transport of quantities such as the magnetic field by irregular flows in the solar photosphere.

[9876947]首席研究员将研究流体运动的数学问题。本文将利用Littlewood-Paley理论和小波的方法研究理想流体不可压缩流动的弱奇异性。欧拉方程的基本非平稳问题将在通常具有无界涡量的函数类中进行研究。他将讨论非规则流的线性矢量传输问题。输运理论的这些方面直接适用于欧拉方程的存在性和唯一性问题。流体运动的数学理论是气象学、地球物理学、天体物理学和数学本身应用的基础。自然界中的大多数流动，如洋流、飓风或星系中的物质运动，都是高度不规则的。奇异结构的起源和演化，如水流的快速振荡，仍然没有得到很好的理解。除此之外，由于流动不断产生的小尺度结构的不稳定性，限制了不规则流动的数值模拟。PI将调查这一主题的两个相关方面。首先，奇点流的基本数学性质。第二，由太阳光球中不规则流引起的量的传输，例如磁场。