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

这个项目集中在非线性偏微分方程领域的两个基本领域。首先，主要研究人员从数值和理论的角度研究三维不可压缩理想流体流动的破裂问题。其次，他计划研究非线性Klein-Gordon方程的一些正则性问题：三维半线性方程的时滞奇性形成和低维整体存在性以及大幅值解的崩溃。这些研究将为空气动力学和波传播等应用领域奠定基础。

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.