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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… Click to show full abstract
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.
Keywords:
diffeomorphism groups;
invariant metric;
one side;
groups one;
side invariant;
stability geodesics
Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2020
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Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!