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

Freddy Bouchet (1)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis

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.

Mots clés: 2D Euler equation; equilibrium statistical mechanics; long range interactions; ensemble equivalence; vortices; jets

Domaines: Mécanique statistique [cond-mat.stat-mech]; Formation de Structures et Solitons [nlin.PS]

Freddy Bouchet. Simpler Variational Problem for Statistical Equilibria of the 2D Euler Equation and Other Systems with Long Range Interactions. 2007. ⟨hal-00182446⟩