Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit

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