Vanishing viscosity in the presence of a boundary

存在边界时粘度消失

• 批准号: 0842408
• 负责人: James Kelliher
• 金额: $ 7.84万
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0842408&HistoricalAwards=false
• 关键词: Vanishing; viscosity; presence; boundary

The purpose of this project is to better understand the behavior of nearly inviscid fluids near a boundary. Such behavior has been of interest to engineers and physicists for at least a hundred years and has been a pressing concern of mathematicians working in fluids for at least half of that time. There is much practical knowledge about the boundary behavior, but little precise mathematical understanding. The proposal is to investigate the boundary behavior of the fluid in the limited setting of a two dimensional bounded domain, focusing on a disk, where important aspects of the analysis are simplified, but where the behavior is still physically relevant. The goal is to strengthen existing partial results concerning the boundary behavior of the fluid and to attempt to integrate the partially heuristic methods of engineers and physicists into a mathematical setting.Many fluids have reasonably low viscosity and nearly all fluids are in contact with a boundary. How is the flow of blood affected by imperfections in vessel walls? How is the lift of a wing determined by its shape? How do a submarine's propellers induce turbulence when running at certain speeds? In all of these problems and many more the flow of the fluid can be constrained by the interaction of the fluid with the boundary in ways that are currently only partially understood. Almost any progress that can be made in the understanding of this interaction would ultimately be beneficial in addressing all of these problems, whether by giving better control on the error bounds in numerical computations, by giving a qualitative understanding of the interaction, or even by demonstrating that the boundary behavior is even more complex than is currently believed.

这个项目的目的是为了更好地了解接近无粘性流体的行为在边界附近。至少一百年来，工程师和物理学家一直对这种行为感兴趣，并且至少有一半的时间是在流体中工作的数学家的迫切关注。有很多关于边界行为的实际知识，但很少有精确的数学理解。该建议是调查的边界行为的流体在有限的设置一个二维有界域，集中在一个磁盘上，其中的重要方面的分析被简化，但其中的行为仍然是物理相关的。我们的目标是加强现有的关于流体边界行为的部分结果，并试图将工程师和物理学家的部分启发式方法整合到一个数学环境中。许多流体具有相当低的粘度，几乎所有的流体都与边界接触。血管壁的缺陷如何影响血液的流动？机翼的升力是如何由它的形状决定的？潜艇的螺旋桨在以一定速度运行时是如何引起湍流的？在所有这些问题和更多的问题中，流体的流动可以通过流体与边界的相互作用以目前仅部分理解的方式来约束。在理解这种相互作用方面所能取得的几乎任何进展最终都将有利于解决所有这些问题，无论是通过更好地控制数值计算中的误差范围，还是通过对相互作用的定性理解，甚至通过证明边界行为比目前认为的更复杂。