A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations

Dan-Virgil Voiculescu

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arXiv · 1902.02442

A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations

Dan-Virgil Voiculescu

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Abstract

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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Dan-Virgil Voiculescu. 2019-02-07. A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations. https://arxiv.org/abs/1902.02442

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