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On ε-approximate singularities of autonomous systems of vortex type

Published online by Cambridge University Press:  22 January 2016

Hideo Omoto  and
Yoshifumi Kimura
Hideo Omoto*
Affiliation:
Department of Mathematics School of Science Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
Yoshifumi Kimura*
Affiliation:
The Institute for Solid State Physics University of Tokyo, Minato-ku, Tokyo 106, Japan
*
Nagoya University College of Medical Technology, Higashi-ku, Nagoya 461, Japan
Nagoya University College of Medical Technology, Higashi-ku, Nagoya 461, Japan
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Let us consider three vortex-filaments zj(t) with strength Γj (j = 1, 2, 3) in the complex plane C. Then the system of motion equations is given by

This system (E) is defined on V = C3 = Δ, where Δ = {(z1 z2, z3) ∈ C3; Zj = zk for j ≠ k} is the super-diagonal set of C3.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 15 - 31
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

[ 1 ] Lamb, H., Hydrodynamics, Cambridge (1932).Google Scholar
[ 2 ] Synge, J. L., On the motion of three vortices, Canad. J. Math., 1 (1949), 257–270.CrossRefGoogle Scholar
[ 3 ] Pontrjagin, L., Ordinary Differential Equations, Kyoritsu (1964).Google Scholar
[ 4 ] Sternberg, S., Lectures on Differential Geometry, Prentice-Hall, New Jersey (1965).Google Scholar