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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

A global theory of steady vortex rings in an ideal fluid


Authors: L. E. Fraenkel and M. S. Berger
Journal: Bull. Amer. Math. Soc. 79 (1973), 806-810
MSC (1970): Primary 35J60, 76C05
MathSciNet review: 0320555
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  • 1. H. von Helmholtz, Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelwegungen entsprechen, Crelle's Journal 55 (1858), 25-55.
  • 2. M. J. M. Hill, On a spherical vortex, Phil. Trans. Roy. Soc. London A185 (1894), 213-245.
  • 3. Leon Lichtenstein, Über einige Existenzprobleme der Hydrodynamik homogener, unzusammendrückbarer, reibungsloser Flüssigkeiten und die Helmholtzschen Wirbelsätze, Math. Z. 23 (1925), no. 1, 89–154 (German). MR 1544733, http://dx.doi.org/10.1007/BF01506223
  • 4. K. Maruhn, Über die Existenz stationärer Bewegungen von Wirbelringen, Proc. Ninth International Congress Appl. Mech., University of Brussels 1 (1957), 173-176.
  • 5. L. E. Fraenkel, On steady vortex rings of small cross-section in an ideal fluid, Proc. Roy. Soc. London A316 (1970), 29-62.
  • 6. J. Norbury, A steady vortex ring close to Hill’s spherical vortex, Proc. Cambridge Philos. Soc. 72 (1972), 253–284. MR 0302044 (46 #1197)
  • 7. M. M. Vainberg, Variational methods for the study of nonlinear operators, Holden-Day Inc., San Francisco, Calif., 1964. With a chapter on Newton’s method by L. V. Kantorovich and G. P. Akilov. Translated and supplemented by Amiel Feinstein. MR 0176364 (31 #638)
  • 8. M. S. Berger, Lectures on nonlinear problems of mathematical analysis (to appear).
  • 9. G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, no. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486 (13,270d)
  • 10. Walter Littman, Generalized subharmonic functions: Monotonic approximations and an improved maximum principle, Ann. Scuola Norm. Sup. Pisa (3) 17 (1963), 207–222. MR 0177186 (31 #1450)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1973-13328-2
PII: S 0002-9904(1973)13328-2