非线性Lyapunov稳定性及Stern's Modons的稳定性判据

NONLINEAR LYAPUNOV STABILITY OF BAROTROPIC ATMOSPHERIC MOTIONS AND STABILITY CRITERION OF STERNS MODONS

本文在构造正压大气运动的浅水波模式的Hamilton守恒量和积分不变的Casimir泛函的基础上,建立了一个积分不变的Lyapunov函数,通过使用变分法,找出了正压旋转流体运动的非线性Lyapunov稳定性判据,并进一步讨论了Stern's Modons的稳定性。

In this paper, the conserved Hamilionian quantity and integral invariant Casimir functional of shallow water wave equation are constructed, and the integral invariant Lyapunov functional, then the nonlinear Lyapunov stability criteria of barotropic rotating fluid are derived. Furthermore, the stability of Stern's Modons is also discussed by the variational method.