华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (3): 23-30.

• 数学 统计学 • 上一篇    下一篇

三维球坐标准地转流的非线性稳定性(英）

蔡景景1,2, 刘永明1,2   

  1. 1. 华东师范大学 数学系, 上海 200062; 2. 华东师范大学 地理信息科学教育部重点实验室, 上海 200062
  • 收稿日期:2006-06-29 修回日期:2006-09-11 出版日期:2007-05-25 发布日期:2007-05-25
  • 通讯作者: 刘永明

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

CAI Jing-jing1,2, LIU Yong-ming1,2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China 2. Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200062, China
  • Received:2006-06-29 Revised:2006-09-11 Online:2007-05-25 Published:2007-05-25
  • Contact: LIU Yong-ming

摘要： 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.

关键词: 非线性稳定性, 准地转流, 球坐标, Poincaré不等式, 非线性稳定性, 准地转流, 球坐标, Poincaré不等式

Abstract: 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.

Key words: quasi-geostrophic motion, spherical geometry, Poincaréinequality, nonlinear stability, quasi-geostrophic motion, spherical geometry, Poincaréinequality

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