论文标题
在三维椭球上的不可压缩欧拉流中存在一个共轭点
Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoid
论文作者
论文摘要
紧凑的riemannian歧管M的容量保护差异群的存在与MISIOLEK曲率不可压缩的EULER方程解决方案的Lagrangian稳定性有关，这是误解的标准，这是对体积分散量的相对差异的差异，这是一个合理的标准方程式。在本文中，我们介绍了一类静止的解决方案，上面涉及一个任意的riemannian歧管，其行为相对于Misiolek曲率很好，并给出了对属于该类别的解决方案的Misiolek曲率的阳性结果。此外，我们还表明了三维椭圆形病例中的共轭点的存在。
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.
