Methods and Applications of Analysis

Volume 11 (2004)

Number 3

A Semi-Analytic Approach to Euler Singularities

Pages: 423 – 430



Russel E. Caflisch

Michael Siegel


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.

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