6 research outputs found
Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoid
The existence of a conjugate point on the volume-preserving diffeomorphism
group of a compact Riemannian manifold M is related to the Lagrangian stability
of a solution of the incompressible Euler equation on M. The Misiolek curvature
is a reasonable criterion for the existence of a conjugate point on the
volume-preserving diffeomorphism group corresponding to a stationary solution
of the incompressible Euler equation. In this article, we introduce a class of
stationary solutions on an arbitrary Riemannian manifold whose behavior is nice
with respect to the Misiolek curvature and give a positivity result of the
Misiolek curvature for solutions belonging to this class. Moreover, we also
show the existence of a conjugate point in the three-dimensional ellipsoid case
as its corollary.Comment: Any comments are appreciate