Journal of East China Normal University(Natural Sc ›› 2007, Vol. 2007 ›› Issue (3): 23-30.

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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

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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