Mathematical Sciences: Asymptotics of Large Scale Behavior and Solutions of PDE's

数学科学：大规模行为的渐进性和偏微分方程的解

• 批准号: 8914420
• 负责人: C. David Levermore
• 金额: $ 4.12万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-01-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8914420&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotics; Large; Scale

This research centers on various asymptotics problems of interest in mechanics and physics, including the zero dispersion limit for several nonlinear wave equations, the recovery of the Navier-Stokes equations from the more general Boltzmann equation, and the incompressible limit of the equations of compressible fluid dynamics. The study of complicated nonlinear phenomena often requires the solution of simplified forms of the governing equations. One of the best ways of achieving this is to use the naturally occurring length and time scales of the problem to simplify the problem while retaining the essential physics. The proposed research will advance our knowledge of fluid flow phenomena by performing this simplification on a number of important problems.

这项研究集中于力学和物理学中感兴趣的各种渐近问题，包括几个非线性波动方程的零色散极限、从更一般的玻尔兹曼方程恢复纳维-斯托克斯方程以及可压缩流体方程的不可压缩极限动力学。 复杂非线性现象的研究常常需要求解简化形式的控制方程。 实现这一目标的最佳方法之一是使用问题自然发生的长度和时间尺度来简化问题，同时保留基本的物理原理。 拟议的研究将通过对许多重要问题进行简化来增进我们对流体流动现象的了解。