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The Robert-Sommeria-Miller equilibrium statistical mechanics predicts thefinal organization of two dimensional flows. This powerful theory is difficultto handle practically, due to the complexity associated with an infinite numberof constraints. Several alternative simpler variational problems, based onCasimir's or stream function functionals, have been considered recently. Weestablish the relations between all these variational problems, justifying theuse of simpler formulations.

Simpler Variational Problem for Statistical Equilibria of the 2D Euler Equation and Other Systems with Long Range Interactions