Mathematical Scienecs: Linear and Nonlinear Waves

数学科学：线性波和非线性波

• 批准号: 9401777
• 负责人: Avraham Soffer
• 金额: $ 5.6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401777&HistoricalAwards=false
• 关键词: Mathematical; Scienecs; Linear; Nonlinear; Waves

9401777 Soffer Two main topics will be investigated. In the Cauchy problem for the nonlinear wave equation, the results of Ginibre-Soffer- Velo on the critical power nonlinear wave equation which are complete for the radial case will be further developed to include the general data. It is based on applying new Lebesgue pth power bounds which allow the control of the p-norm of a function in terms of singular weighted norms and partial regularity. In the theory of three body dispersive systems a new class of dilations, deformed by various partitions of unity to cluster decompositions will be used. This will allow proofs of local decay and other spectral properties of three body dispersive equations. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concept of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single force. ***

9401777 sofffer将调查两个主要主题。在非线性波动方程的Cauchy问题中，将进一步发展ginibre - soft - Velo关于临界功率非线性波动方程的完整结果，以包括一般数据。它基于应用新的Lebesgue p次幂界，该界允许用奇异加权范数和部分正则性来控制函数的p范数。在三体色散系统的理论中，将使用一类新的膨胀，它由统一的各种划分变形为簇分解。这将允许证明局部衰减和三体色散方程的其他谱性质。现代物理学，量子力学和相对论，是二十世纪的产物。它牢固地建立在上个世纪对物质微观结构的研究和对超距作用、电磁和热辐射等概念的理解上。这些发展的数学基础统称为数学物理学，范围从控制粒子动力学的薛定谔算符的详细分析，到试图将四种已知力统一为单一力的统一场论。＊＊＊