Self-similar singularities of the 3D Euler equations

Self-similar solutions are considered to the incompressible Euler equations in , where the similarity variable is defined as , β ≥ 0. It is shown that the scaling exponent is bounded above: β ≤ 1. Requiring |u| 2 < ∞ and allowing more than one length scale, it is found β ϵ [2/5, 1]. This new result on the self-similar singularity is consistent with known analytical results for blow-up conditions.