Mathematical Sciences: The Stellar Dynamics of Galaxies, andNonlinear Effects in Low Reynolds Number Flow

这个多主题研究计划的单一数学主题是第一类奇异积分方程，其分析是已知的困难。研究的一个子领域是关于这类方程的非唯一解。在另一个子领域，要解决的问题是PI开发的迭代过程的收敛区域。研究结果将对几个应用领域产生直接影响。其一是有多种方法可以从具有正确总质量分布的不同恒星轨道构建椭圆星系的自洽三轴模型。另一种是通过刚性物体（如水下潜艇）的缓慢粘性流。

The single mathematical theme of this multiple topic research program is singular integral equations of the first kind, the analysis of which is known to be difficult. One subarea of the research is concerned with the nonunique solutions of such equations. In another subarea, the issue to be resolved is the region of convergence of the iterative procedure devloped by the PI. The research rersults will have immediate implications on several application areas. One is the variety of ways in which self-consistent triaxial models of elliptical galaxies can be constructed from different stellar orbits with the correct total mass distribution. Another is slow viscous flow past rigid bodies such underwater submarines.