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This is a joint work with T.Elgindi and N.Masmoudi. Recently Elgindi proved the existence of a continuum of $C^{1,\alpha}$ 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 $C^{1,\alpha}$ selfsimilar solutions. In a second part I will explain how those one dimensional models helped us understanding the full 3D axisymmetric Euler.