华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (2): 24-30.

• 数学 统计学 • 上一篇    下一篇

一个最优的Poincaré不等式

刘永明， 李 娜   

  1. 华东师范大学 数学系，上海 200062
  • 收稿日期:2002-06-28 修回日期:2003-10-24 出版日期:2004-06-25 发布日期:2004-06-25
  • 通讯作者: 刘永明

An Optimal Poincaré Inequality

LIU Yong-ming, LI Na   

  1. Department of Mathematics, East China Normal University, Shanghai 200062， China
  • Received:2002-06-28 Revised:2003-10-24 Online:2004-06-25 Published:2004-06-25
  • Contact: LIU Yong-ming

摘要： 在Arnold的非线性稳定性理论中，Poincaré积分不等式起着关键性的作用.该文给出了二维准地转流中估计扰动能量的上界时要用到的一个最好可能的Poincaré积分不等式.可用它来得到更好的非线性判据和更精细的扰动能量的上界.

关键词: Poincaré不等式, 变分原理, Fourier分析, 非线性稳定性, Poincaré不等式, 变分原理, Fourier分析, 非线性稳定性

Abstract: Poincaré integral inequality plays an inportant role in the nonlinear stability theorem of Arnold. In this paper, a best possible Poincaré integral inequality is obtained, which can be used to get a better estimation of disturbance bound for two-dimensional quasi-geostrophic flow and a better nonlinear stability criterion as well.

Key words: variational principle, Fourier analysis, nonlinear stability, Poincaré inequality, variational principle, Fourier analysis, nonlinear stability

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