| Abstract: | 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. |
