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