On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations

Abstract

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.

arXiv comment21 pages

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