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We prove that any weak space-time $L^2$ vanishing viscosity limit of asequence of strong solutions of Navier-Stokes equations in a bounded domain of${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' localenstrophies are uniformly bounded. We also prove that $t-a.e.$ weak $L^2$inviscid limits of solutions of 3D Navier-Stokes equations in bounded domainsare weak solutions of the Euler equation if they locally satisfy a scalingproperty of their second order structure function. The conditions imposed arefar away from boundaries, and wild solutions of Euler equations are not apriori excluded in the limit.

Remarks on high Reynolds numbers hydrodynamics and the inviscid limit