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

这个多重主题中的单一数学主题 研究方案是奇异积分方程的 第一种，已知其分析是困难的。 该研究的一个子领域涉及非唯一性 这些方程的解。 在另一个分领域， 求解的是迭代过程的收敛区域 由PI开发。 研究结果将直接影响到 几个应用领域。 一个是各种方式， 椭圆星系的自洽三轴模型 可以从不同的恒星轨道构建， 正确的总质量分布。 另一种是慢粘性流 而不是像水下潜艇这样的刚体。

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.