LAUSR

We prove that any weak space-time $$L^2$$L2 vanishing viscosity limit of a sequence of strong solutions of Navier–Stokes equations in a bounded domain of $${\mathbb R}^2$$R2 satisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove that $$t-a.e.$$t-a.e. weak $$L^2$$L2 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.