自由概率中的流体力学习题：建立自由欧拉方程
A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations
摘要：
对于具有Gauss测度的欧几里得空间的自由概率模拟，我们应用Arnold方法导出了非交换向量场李代数的保迹Euler方程.我们将方程推广到满足非交换光滑性要求的向量场。我们引入一个循环涡度，并证明它满足涡度方程，它产生一个家庭的保守量。
英文摘要：
For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend the equations to vector fields satisfying non-commutative smoothness requirements. We introduce a cyclic vorticity and show that it satisfies a vorticity equation and that it produces a family of conserved quantities.
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