This paper reviews the efforts to construct (or prove the impossibility of) singular solutions of the Euler equations for three dimensional incompressible flow. A semi-analytic approach to this problem is formulated based on numerical computation of complex traveling wave solutions, followed by perturbation construction of a real solution, for axisymmetric flow with swirl. The perturbation analysis depends on small amplitude of the singularity in the traveling wave solution, for small swirl in the underlying background flow.
"A Semi-Analytic Approach to Euler Singularities." Methods Appl. Anal. 11 (3) 423 - 430, September 2004.