×

zbMATH — the first resource for mathematics

On the bifurcation of steady vortex rings from a Green function. (English) Zbl 0853.35135
The author considers the steady vortex rings in an ideal fluid. Two main results are obtained:
Three properties of the stream function (due to vorticity) are established for a large value of flux. It is shown that the ratio of stream function to circulation of the vortex ring bifurcates from a Green function as the flux decreases from infinity.
Reviewer: V.A.Sava (Iaşi)

MSC:
35R35 Free boundary problems for PDEs
76B47 Vortex flows for incompressible inviscid fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fraenkel, Proc. Roy. Soc 88 pp 267– (1981) · Zbl 0466.31007 · doi:10.1017/S0308210500020114
[2] Edmunds, Spectral Theory and Differential Operators (1987) · Zbl 0628.47017
[3] DOI: 10.1007/BF01982715 · Zbl 0454.35087 · doi:10.1007/BF01982715
[4] DOI: 10.1007/BF00251252 · Zbl 0609.76018 · doi:10.1007/BF00251252
[5] Widman, Math. Scan 21 pp 17– (1967) · Zbl 0164.13101 · doi:10.7146/math.scand.a-10841
[6] DOI: 10.1090/S0002-9904-1953-09651-3 · Zbl 0053.25303 · doi:10.1090/S0002-9904-1953-09651-3
[7] DOI: 10.1007/BF02392107 · Zbl 0282.76014 · doi:10.1007/BF02392107
[8] DOI: 10.1017/S0022112073001266 · Zbl 0254.76018 · doi:10.1017/S0022112073001266
[9] Nirenberg, Ann. Scuola Norm. Sup 3 pp 115– (1959)
[10] DOI: 10.1002/cpa.3160280602 · Zbl 0338.76015 · doi:10.1002/cpa.3160280602
[11] Ni, J. d’Analyse Math 37 pp 208– (1980)
[12] Lamb, Hydrodynamics (1932)
[13] Jung, J. Reine Angew. Math 123 pp 241– (1901)
[14] Watson, Theory of Bessel Functions (1952)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.