Some positivity results of the curvature on the group corresponding to the incompressible Euler equation with Coriolis force

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 positi…

二维和三维欧拉方程的精确非稳态解

Exact non-stationary solutions of the Euler equations in two and three dimensions

本文基于Arnold几何框架，提出构造不可压缩欧拉方程精确光滑全局解的方法，涵盖经典解如凯尔文波和罗斯比-豪尔维茨波，并在曲面和三维流形上产生新解，同时对二维和三维流形进行分类。