×

zbMATH — the first resource for mathematics

Isoperimetric inequalities for the energy of uniform-vorticity flows in channels of uniform width. (English) Zbl 0951.76078
The main results of this paper are isoperimetric inequalities concerning the dependence of the kinetic energy of the constant-vorticity flows in a uniform channel on its width and on the length of its middle axis.
MSC:
76M30 Variational methods applied to problems in fluid mechanics
76D17 Viscous vortex flows
76B47 Vortex flows for incompressible inviscid fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Acker, SIAM J. Math. Anal. 9 pp 1179– (1978) · Zbl 0335.31002
[2] ?Some free boundary optimization problems and their solutions?, in: Numerische Behandlung von Differentialgleichungen mit besonderer Berucksichtigung freier Randwertaufgaben, ( and eds), pp. 9-22, Birkhauser, Basel, 1978.
[3] Acker, SIAM J. Math. Anal. 12 pp 169– (1981) · Zbl 0456.49007
[4] Carleman, Math. Z. 1 pp 208– (1918) · JFM 46.0765.02
[5] Korevaar, Arch. Rational Mech. Anal. 97 pp 19– (1987) · Zbl 0624.35031
[6] Payne, SIAM Rev. 9 pp 453– (1967) · Zbl 0154.12602
[7] and Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, vol. 27, Princeton University Press, Princeton, N. J., 1951. · Zbl 0044.38301
[8] ?Einfache Beweis der isoperimetrischen Hauptsätze?, Jacob Steiner’s Gesammelte Werke, (herausgegeben von K. Weierstrass), pp. 75-91, Druck und Verlag von G. Reimer, Berlin. 1881, Band II.
[9] Szegö, Math. Z. 33 pp 419– (1931) · Zbl 0001.07001
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.