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We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which approximates the dynamics of the Euler equations on the solid boundary of a cylindrical domain. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find are consistent with direct simulation of the model and enjoy some stability property.

Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations