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

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• Milo Viviani (Scuola Normale Superiore di Pisa)
• Wednesday 31 August 2022, 12:00-12:20
• No Room Required.

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GFDW01 - Mathematics of geophysical fluid dynamic models of intermediate complexity: qualitative and statistical behaviour

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 $\mathbb{S}^2$, 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. Co-Authors: Franco Flandoli and Umberto Pappalettera

This talk is part of the Isaac Newton Institute Seminar Series series.

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