A SPECIAL-CLASS OF STATIONARY FLOWS FOR 2-DIMENSIONAL EULER EQUATIONS- A STATISTICAL-MECHANICS DESCRIPTION .2.

We continue and conclude our analysis started in Part I (see [CLMP]) b y discussing the microcanonical Gibbs measure associated to a N-vortex system in a bounded domain. We investigate the Mean-Field limit for s uch a system and study the corresponding Microcanonnical Variational P rinciple for the Mean-Field equation. We discuss and achieve the equiv alence of the ensembles for domains in which we have the concentration at beta --> (-8 pi)(+) in the canonical framework. In this case we ha ve the uniqueness of the solutions of the Mean-Field equation. For the other kind of domains, for large values of the energy, there is no eq uivalence, the entropy is not a concave function of the energy, and th e Mean-field equation has more than one solution. In both situations, we have concentration when the energy diverges. The Microcanonical Mea n Field Limit for the N-vortex system is proven in the case of equival ence of ensembles.