Nonlinear Stability for Eady’s Model
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摘要: Poincaré型的积分不等式在三维准地转流的(在Arnold第二定理意义下的)非线性稳定性的研究中起着重要的作用．周期带域上Eady模型是该方法的应用中最重要的一种情况,但至今所得的最好的非线性稳定性条件和线性稳定的条件不一致，两者仅在带域的周期无限大时才一致．为解决这个差异, 利用周期带域上的Eady模型的动量守衡的性质，通过变分方法和积分的精细估计，建立一个加强的Poincaré积分不等式，从而证明了Eady模型的线性稳定意味着非线性稳定．
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关键词:
- Poincaré不等式 /
- Eady模型 /
- 非线性稳定性
Abstract: Poincar type integral inequality plays an important role in the study of nonlinear stability (in the sense of Arnold's second theorem) for three-dimensional quasi-geostophic flow.The nonlinear stability of Eady's model is one of the most important cases in the application of the method.But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident.The two criteria coincide only when the period of the channel is infinite.To fill this gap,the enhanced Poincar inequality was obtained by considering the additional conservation law of momentum and by rigorous estimate of integral inequality.So the new nonlinear stability criterion was obtained,which shows that for Eady's model in the periodic channel,the linear stable implies the nonlinear stable.-
Key words:
- Poincar inequality /
- Eady's model /
- nonlinear stability
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