This is a joint work with T.Elgindi and N.Masmoudi. Recently Elgindi proved the existence of a continuum of C1,α self similar solutions to 3D axisymmetric Euler equations with vanishing swirl. The aim of the talk will be to show that those solutions are stable under perturbations with swirl. I will in a first part of my presentation talk about recent result we obtained on one dimensional models for which we proved the stability of smooth and C1,α selfsimilar solutions. In a second part I will explain how those one dimensional models helped us understanding the full 3D axisymmetric Euler.