Asymptotic Problems in Fluid Mechanics, Gas Dynamics and Quantum Mechanics

流体力学、气体动力学和量子力学中的渐近问题

• 批准号: 0403983
• 负责人: Nader Masmoudi
• 金额: $ 14.25万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0403983&HistoricalAwards=false
• 关键词: Asymptotic; Problems; Fluid; Mechanics; Gas

Proposal DMS-0403983PI: Nader Masmoudi, Courant Institute-NYUTitle: Asymptotic problems in fluid mechanics, gas dynamics and quantum mechanicsABSTRACTThe Principal Investigator (PI) proposes to continue working onsome asymptotic problems coming from Fluid Mechanics, GasDynamics and Quantum Mechanics. These asymptotic problems arisewhen a dimensionless parameter (such as the Reynolds number, theMach number or a time scaling) goes to zero or to infinity. Instudying these problems, many mathematical difficulties arise.These difficulties are mainly due to the change of the type ofthe equations, the presence of many temporal and spatial scales,the presence of resonances, the presence of boundary layers ...Many tools have been developed to circumvent these difficultiessuch as the introduction of different types of measures todescribe the defect of strong convergence, the use of compensated compactness type arguments, the use of averaging lemma, the use ofenergy methods and relative entropy methods ... Of course, manyother tools should be developed in the future. More specificallythe PI plans to continue working on the hydrodynamic limits ofthe Boltzmann equation when the Knudsen number goes to 0especially in bounded domains and relate this to some of the knownresults in the compressible-incompressible limit. He also plans tolook at the limit when the Weber number goes to infinity in thewater wave problem.The PI proposes to study some asymptotic problems coming fromFluid Mechanics, Gas Dynamics and Quantum Mechanics. The study ofthese asymptotic problems is very important to get a betterunderstanding about the behavior of complicated systems indifferent limiting cases. This also allows to have a betterunderstanding of the real physical phenomenon taking place.Moreover, it provides a way of giving rigorous derivations ofdifferent physical models. It also gives a better knowledge aboutthe domain of validity of each simplifying model. This is veryimportant for engineers and physicists who are looking for thesimplest model that captures the phenomenon to implementnumerically or to apply in real life.

提案DMS-0403983PI：纽约大学库兰特研究所的纳德·马斯穆迪题目：流体力学、气体动力学和量子力学中的渐近问题摘要首席研究员(PI)建议继续研究来自流体力学、气体动力学和量子力学的一些渐近问题。当一个无量纲参数(如雷诺数、马赫数或时间标度)变为零或无穷大时，就会出现这些渐近问题。在研究这些问题时，出现了许多数学困难。这些困难主要是由于方程类型的变化，存在许多时间和空间尺度，存在共振，存在边界层.许多工具已经被开发出来来规避这些困难，例如引入不同类型的措施来描述强收敛的缺陷，使用补偿紧致型变元，使用平均引理，使用能量方法和相对熵方法...当然，未来还需要开发更多其他工具。更具体地说，当Knudsen数变为0时，PI计划继续研究Boltzmann方程的流体力学极限，特别是在有界区域，并将其与可压缩-不可压缩极限中的一些已知结果联系起来。他还计划研究水波问题中Weber数趋于无穷大时的极限。Pi建议研究流体力学、气体动力学和量子力学中的一些渐近问题。对这些渐近问题的研究对于更好地理解复杂系统在不同极限情况下的行为是非常重要的。这也允许对发生的真实物理现象有更好的理解。此外，它还提供了一种给出不同物理模型的严格推导的方法。它还给出了关于每个简化模型的有效性领域的更好的知识。这对于工程师和物理学家来说是非常重要的，他们正在寻找最简单的模型来实现这一现象，或者将其应用于现实生活。