一个最优的Poincaré不等式

An Optimal Poincare Inequality

在Arnold的非线性稳定性理论中,Poincare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Poincare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。

Poincare integral inequality plays an inportant role in the nonlinear stability theorem of Arnold. In this paper, a best possible Poincare 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.