A Note on the Stability of Geodesics on Diffeomorphism Groups with One-side Invariant Metric  

作　　者：Li Juan ZHOU 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 0010021,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第5期620-630,共11页数学学报（英文版）

基　　金：supported by Education Department of Inner Mongolia Autonomous Region(Grant No.NJZY20004);NSFC(Grant No.11671392)。

摘　　要：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.

关 键 词：Volume-preserving DIFFEOMORPHISM GROUP Bott-Virasoro GROUP Euler equation GEODESIC Eulerian INSTABILITY Lagrangian INSTABILITY 

分 类 号：O152.7[理学—数学]