Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Rearrangements in steady vortex flows with circulation
HTML articles powered by AMS MathViewer

by Alan R. Elcrat and Kenneth G. Miller PDF
Proc. Amer. Math. Soc. 111 (1991), 1051-1055 Request permission

Abstract:

It is shown that a steady two-dimensional flow, in which a finite vortex is in equilibrium with the irrotational flow past an obstacle, can be obtained as the solution of a variational problem in the class of rearrangements of a fixed function in ${L^p}$. The main step is to establish a bound on the support of the vorticity. The advantage of this approach, as in the recent works of Burton, Benjamin, and Auchmuty, is that the profile function of the vorticity is determined by the rearrangement class in which solutions are sought.
References
  • V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391
    • J. F. Auchmuty and T. B. Benjamin, unpublished manuscript.
  • T. Brooke Benjamin, The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics, Applications of methods of functional analysis to problems in mechanics (Joint Sympos., IUTAM/IMU, Marseille, 1975) Lecture Notes in Math., vol. 503, Springer, Berlin, 1976, pp. 8–29. MR 0671099
  • H. J. Brascamp, Elliott H. Lieb, and J. M. Luttinger, A general rearrangement inequality for multiple integrals, J. Functional Analysis 17 (1974), 227–237. MR 0346109, DOI 10.1016/0022-1236(74)90013-5
  • G. R. Burton, Steady symmetric vortex pairs and rearrangements, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), no. 3-4, 269–290. MR 943803, DOI 10.1017/S0308210500014669
  • G. R. Burton, Variational problems on classes of rearrangements and multiple configurations for steady vortices, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 4, 295–319 (English, with French summary). MR 998605
  • Alan R. Elcrat and Kenneth G. Miller, Steady vortex flows with circulation past asymmetric obstacles, Comm. Partial Differential Equations 12 (1987), no. 10, 1095–1115. MR 886341, DOI 10.1080/03605308708820520
  • Bruce Turkington, On steady vortex flow in two dimensions. I, II, Comm. Partial Differential Equations 8 (1983), no. 9, 999–1030, 1031–1071. MR 702729, DOI 10.1080/03605308308820293
    • —, On steady vortex flows in two dimensions, II, Comm. Partial Differential Equations 8 (1983), 1031-1071.
  • Bruce Turkington, On the evolution of a concentrated vortex in an ideal fluid, Arch. Rational Mech. Anal. 97 (1987), no. 1, 75–87. MR 856310, DOI 10.1007/BF00279847
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35Q35, 58D25, 76C05
  • Retrieve articles in all journals with MSC: 35Q35, 58D25, 76C05
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 111 (1991), 1051-1055
  • MSC: Primary 35Q35; Secondary 58D25, 76C05
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1043409-2
  • MathSciNet review: 1043409