Existence of a Conjugate Point in the Incompressible Euler Flow on a Three-Dimensional Ellipsoid

被引：0
|
作者：
Lichtenfelz L.A. [1 ]
Tauchi T. [2 ]
Yoneda T. [3 ]
机构：
[1] Department of Mathematics, Wake Forest University, 127 Manchester Hall, Box 7388, Winston-Salem, 27109, NC
[2] Department of Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Kanagawa, Sagamihara-shi
[3] Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Tokyo, Kunitachi
来源：
Arnold Mathematical Journal | 2024年 / 10卷 / 2期
基金：
日本学术振兴会;
关键词：
Conjugate point; Diffeomorphism group; Euler equation; Zonal flow;
D O I：
10.1007/s40598-023-00238-1
中图分类号：
学科分类号：
摘要：
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 Misiołek 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 Misiołek curvature and give a positivity result of the Misiołek 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. © 2023, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
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页码：281 / 307
页数：26
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