三维球坐标准地转流的非线性稳定性(英文)

Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions in Spherical Geometry

利用变分原理,对三维球坐标下的准地转流,建立了优化的Poincaré不等式,从而得到了优于以前结果的非线性稳定性定理。并建立了关于扰动能量,扰动拟能及扰动边界能上界的精细的显式估计。

A nonlinear stability theorem was established for three-dimensional quasi- geostrophic motions in spherical geometry by establishing an optimal Poincaré inequality. The inequality was derived by variational principle. The result was shown better than the known results. Moreover, explicit upper bounds for the disturbance energy, the disturbance potential enstrophy, and the disturbance boundary energy on the rigid lids were also established.