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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Stationary configurations of point vortices
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by Kevin Anthony O’Neil PDF
Trans. Amer. Math. Soc. 302 (1987), 383-425 Request permission


The motion of point vortices in a plane of fluid is an old problem of fluid mechanics, which was given a Hamiltonian formulation by Kirchhoff. Stationary configurations are those which remain self-similar throughout the motion. Results of two types are presented. Configurations which are in equilibrium or which translate uniformly are counted using methods of algebraic geometry, which establish necessary and sufficient conditions for existence. Relative equilibria (rigidly rotating configurations) which lie on a line are studied using a topological construction applicable to other power-law systems. Upper and lower bounds for such configurations are found for vortices with mixed circulations. Arrangements of three vortices which collide in finite time are well known. One-dimensional families of such configurations are shown to exist for more than three vortices. Stationary configurations of four vortices are examined in detail.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 383-425
  • MSC: Primary 76C05; Secondary 58F05, 58F40
  • DOI:
  • MathSciNet review: 891628