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

Abstract: In this talk 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 of the Euler equations with marginals distributed as the enstrophy measure. The method relies on nontrivial computations on the structure constants of the Poisson algebra of functions on S², that appear to be new. Finally, we discuss the problem of extending our results to Gibbsian measures associated with higher Casimirs, via Zeitlin’s model.