Mathematical Scienecs: Linear and Nonlinear Waves

小行星9401777 将研究两个主要课题。在非线性波动方程的Cauchy问题中，Ginibre-Soffer- Velo关于临界幂次非线性波动方程的结果在径向情况下是完备的，将进一步发展到包括一般数据。它是基于应用新的Lebesgue第p次权力的界限，允许控制的p-范数的一个功能的奇异加权规范和部分正则性。在三体色散系统的理论中，将使用一类新的膨胀，由各种单位分解变形为簇分解。这将允许证明本地衰减和其他光谱性质的三体色散方程。 现代物理学，量子力学和相对论，是二十世纪的产物。它是建立在上个世纪试图解决物质的微观结构和掌握的概念，在一个距离，电磁，和热辐射。这些发展的数学基础统称为数学物理学，范围从薛定谔算子的详细分析，它支配着粒子的动力学，到统一场论，它试图将四种已知的力统一为一种力。 ***

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. ***