Methods and Applications of Analysis

Volume 11 (2004)

Number 3

A Semi-Analytic Approach to Euler Singularities

Pages: 423 – 430

DOI: http://dx.doi.org/10.4310/MAA.2004.v11.n3.a12

Authors

Russel E. Caflisch

Michael Siegel

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.

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