Mathematical Sciences: Regularity Properties of Ideal Flow and Nonlinear Waves.

数学科学：理想流和非线性波的规律性。

• 批准号: 9102421
• 负责人: Thomas Sideris
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102421&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Regularity; Properties; Ideal

This project is focussed on two basic areas in the field of nonlinear partial differential equations. First, the principal investigator aims to study the question of breakdown of three- dimensional incompressible and ideal fluid flow from the numerical and theoretical point of view. Second, he plans to investigate some regularity questions for the nonlinear Klein-Gordon equation: delayed singularity formation and global existence in low dimensions and breakdown of large amplitude solutions to three-dimensional semilinear equations. These studies will accrue to the foundations of applied areas such as aerodynamics, and wave propagation.

这个项目的重点是在非线性偏微分方程领域的两个基本领域。首先，主要研究者的目的是研究问题的崩溃三维不可压缩和理想的流体流动从数值和理论的观点。其次，他计划研究非线性Klein-Gordon方程的一些正则性问题：延迟奇点的形成和低维的全局存在性，以及三维半线性方程大振幅解的分解。这些研究将为空气动力学和波传播等应用领域奠定基础。