Mathematical Sciences: Stability Problems in Stellar Dynamics and Vortex Dynamics

这个项目涉及两个问题的稳定性分析：一个是无碰撞恒星动力学问题，另一个是不可压缩流体流动问题。在前一种情况下，我们将使用能量Casimir方法来考察非球面星系模型的稳定性。在后一种情况下，哈密顿系统和对称性的思想将被用来研究平面应变流动中基达周期椭圆涡旋的非线性稳定性，并应用于海洋中三维涡旋结构的研究。

This project involves the stability analysis of two problems: one in collisionless stellar dynamics and the other in incompressible fluid flows. In the former case, the energy- Casimir method will be used to examine the stability properties of non-spherical galactic models. In the latter case, ideas form Hamiltonian systems and symmetries will be used to examine the nonlinear stability of Kida's periodic elliptic vortices in a planar straining flows, with applications to a study of three- dimensional vortex structures in the oceans.