论文标题
在区域保护差异组上的共轭点标准
Conjugate point criteria on the area-preserving diffeomorphism group
论文作者
论文摘要
本文回答了一些关于沿着测量学的共轭点的问题，该问题与稳定的2D Euler流相对应，这是由Drivas-Misiolek-Shi-Yoneda的论文提出的。我们提出了一个新的足够标准，以实现共轭点的存在，该标准在Misiolek的标准上提高了。它适用于稳定的2D Euler流动的任何旋转电池，在旋转对称性的情况下，它捕获了所有已知的共轭点。我们给出了表面的一般结构，该表面接收具有给定区域形式，速度曲线和涡度轮廓的稳定流体，从中我们显示了如何在稳定流动的单个旋转单元中检测共轭点。当速度轮廓具有局部极值时，标准变得特别简单。提供了几个示例，在附录中，我们使用Misiołek标准提供了一些新的示例，以沿着Kolmogorov沿着Kolmogorov流动的共轭点进行一些新的例子。
This paper answers some questions about conjugate points along the geodesics corresponding to steady 2D Euler flows, posed by a paper of Drivas-Misiolek-Shi-Yoneda. We present a new sufficient criterion for the existence of conjugate points, which improves on the criterion of Misiolek. It applies in any rotational cell of a steady 2D Euler flow, and in case of rotational symmetry it captures all known conjugate points. We give a general construction of the surfaces that admit a steady fluid with given area form, velocity profile, and vorticity profile, and from this we show how to detect conjugate points in a single rotational cell of a steady flow. When the velocity profile has a local extremum, the criterion becomes particularly simple. Several examples are provided, and in an appendix we use the Misiołek criterion to give some new examples of conjugate points along Kolmogorov flows on the torus.
