We star with the 2D Euler equations and address the question stated in the paper Weak solutions, Renormalized Solutions and Enstrophy Defects in 2D Turbulence by Lopes-Mazzucato-Lopes, whether vanishing viscosity limit give rise to renormalized solutions of the vorticity equation. We give a positive answer to this question even when the initial vorticity is only $L^1$. In the second part of the talk we investigate renormalization properties and energy conservation for the 3D axisymmetric Euler equations.

The talk is based on joint works with G.Crippa, C.Seis and S.Spirito.