Journal of Statistical Physics, Vol. 122, No. 4, February 2006. p. 597-616.
DOI: 10.1007/s10955-005-8011-0
In this article we study the class of the microcanonical invariant measures for the 2D Euler equation under periodic boundary conditions and show that these measures are different from those that are the limits of the stationary measures for randomly forced 2D Navier-Stokes equation as the viscosity tends to zero.