A Semi-Analytic Approach to Euler Singularities

Abstract

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.