Mathematical Sciences: The Partial Differential Equations ofFluid Dynamics and their Numerical Approximation

数学科学：流体动力学偏微分方程及其数值逼近

• 批准号: 8702864
• 负责人: Andrew Majda
• 金额: $ 14.87万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702864&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Partial; Differential; Equations

The PI will continue his research program on partial differential equations of fluid dynamics in several directions involving both compressible and incompressible flows. As primary goals, he will focus on the following four topics: 1. Classical weak solutions and measure-valued solutions of the incompressible Euler equations in 2 and 3 dimensions. 2. Breakdown of smooth solutions for the 3-D Euler equations. 3. Multi-dimensional conservation laws and geometric shock dynamics. 4. Nonlinear development of instabilities in supersonic shear layers. The research is in the general area of applied nonlinear analysis which is currently an important and active research area of applied mathematics. The mixture of analytical and numerical approaches to the solutions of research problems enhances the success potential of the research program. One can expect research results from the program with significant impact on both the mathematical science community and the general science and engineering community.

PI将继续他在几个方向上的流体动力学偏微分方程组的研究计划，包括可压缩和不可压缩流动。作为主要目标，他将专注于以下四个主题：1.二维和三维不可压缩Euler方程的经典弱解和测值解。2.三维Euler方程光滑解的分解。3.多维守恒定律和几何激波动力学。4.超音速剪切层中不稳定性的非线性发展。这项研究属于应用非线性分析的一般领域，它是当前应用数学的一个重要而活跃的研究领域。解决研究问题的分析方法和数值方法的混合提高了研究计划的成功潜力。人们可以期待该计划的研究结果对数学科学界和普通科学和工程界产生重大影响。