A Note on the Stability of Geodesics on Diffeomorphism Groups with One-side Invariant Metric
A Note on the Stability of Geodesics on Diffeomorphism Groups with One-side Invariant Metric
复制标题
具有单边不变度量的微分同胚群测地线稳定性的注解
DOI：
10.1007/s10114-020-8036-y
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Li Zhou
中科院分区：
文献类型：
--
作者：
Li Zhou
本文研究了具有单侧不变度量的保体积自同构群上测地线的稳定性。我们证明了在三维紧致流形上，对于非Beltrami场，不存在拉格朗日指数不稳定的欧拉稳定流。我们注意到，对应于KdV方程的定常流可以是欧拉稳定的，而流体的相应运动至多是指数不稳定的。
In this note, we consider the stability of geodesics on volume-preserving diffeomorphism groups with one-side invariant metric. We showed that for non-Beltrami fields on a three-dimensional compact manifold, there does not exist Eulerian stable flow which is Lagrangian exponential unstable. We noticed that a stationary flow corresponding to the KdV equation can be Eulerian stable while the corresponding motion of the fluid is at most exponentially unstable.