论文标题
剂量的可集成液的拓扑结构
The topology of Bott integrable fluids
论文作者
论文摘要
我们在每个可以存在的每个三个manifold中构建了具有分析性bernoulli函数的Euler方程（对于某些度量）的非变化稳定解：图形歧管。使用可积分系统的理论，任何可接受的摩尔斯 - 摩托函数都可以实现为某些不变稳定的Euler流的伯努利函数。这可以解释为Arnold结构定理的一个反问题，并将其作为必然的解决方案的拓扑分类。最后，我们证明拓扑障碍物在没有非悬念假设的情况下存在：稳定的Euler流具有Morse-Bott Bernoulli功能，仅在图三序列上存在。
We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using the theory of integrable systems, any admissible Morse-Bott function can be realized as the Bernoulli function of some non-vanishing steady Euler flow. This can be interpreted as an inverse problem to Arnold's structure theorem and yields as a corollary the topological classification of such solutions. Finally, we prove that the topological obstruction holds without the non-vanishing assumption: steady Euler flows with a Morse-Bott Bernoulli function only exist on graph three-manifolds.
