论文标题
关于Zeitlin 2D Euler方程的不变度量和解决方案的无限尺寸限制
On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations
论文作者
论文摘要
在这项工作中，我们考虑了Zeitlin V. Zeitlin提出的球体上2D Euler方程的有限维近似，并将其融合向解决方案的解决方案，其边缘分布为endrophy量。该方法依赖于$ \ mathbb {s}^2 $的结构常数的非平凡计算，这似乎是新的。在最后一部分中，我们讨论了将结果扩展到与较高Casimirs相关的Gibbsian措施的问题。
In this work we consider a finite dimensional approximation for the 2D Euler equations on the sphere, proposed by V. Zeitlin, and show their convergence towards a solution to Euler equations with marginals distributed as the enstrophy measure. The method relies on nontrivial computations on the structure constants of $\mathbb{S}^2$, that appear to be new. In the last section we discuss the problem of extending our results to Gibbsian measures associated with higher Casimirs.
