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

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

2007-10-26

arxiv.org/abs/0710.5094v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, submited to Physica D

Scientific paper

10.1016/j.physd.2008.02.029

The Robert-Sommeria-Miller equilibrium statistical mechanics predicts the final organization of two dimensional flows. This powerful theory is difficult to handle practically, due to the complexity associated with an infinite number of constraints. Several alternative simpler variational problems, based on Casimir's or stream function functionals, have been considered recently. We establish the relations between all these variational problems, justifying the use of simpler formulations.

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