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Cipriano, F. "The two dimensional Euler equation: A statistical study." COMMUNICATIONS IN MATHEMATICAL PHYSICS. 201 (1999): 139-154. Abstract

{We construct surface type measures on the level sets for the renormalized energy, which is an invariant quantity for the two dimensional periodic Euler flow, and prove the existence of weak solutions living on such level sets. Other classes of invariant measures for the motion are also introduced.}