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

本课题主要关注非线性偏微分方程领域的两个基本领域。首先，从数值和理论的角度研究三维不可压缩和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：低维延迟奇点形成和整体存在性以及三维半线性方程大振幅解的分解。这些研究将积累为应用领域的基础，如空气动力学和波传播。

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.