Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T09:44:12.064Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence of seamount steady vortex flows

Published online by Cambridge University Press:  17 February 2009

B. Emamizadeh  and
F. Bahrami
B. Emamizadeh
Affiliation:
Department of Mathematics, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAE; e-mail: [email protected].
F. Bahrami
Affiliation:
Department of Mathematics, Tarbiat Modarres University, P.O. Box 14155-4838, Tehran, Iran. Current address: Department of Mathematics, Tabriz University, Tabriz, Iran; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we will study a feature of a localised topographic flow. We will prove existence of an ideal fluid containing a bounded vortex, approaching a uniform flow at infinity and passing over a localised seamount. The domain of the fluid is the upper half-plane and the data prescribed is the rearrangement class of the vorticity field.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 1 , July 2005 , pp. 75 - 88
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Adams, R. A., Sobolev spaces, Pure and Appl. Math. 65 (Academic Press, New York, 1975).Google Scholar
[2]Benjamin, T. B., “The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics”, in Applications of methods of functional analysis to problems in mechanics, Lecture Notes in Math. 503, (Springer, Berlin, 1976) 8–29.CrossRefGoogle Scholar
[3]Burton, G. R., “Rearrangements of functions, maximization of convex functionals and vortex rings”, Math. Ann. 276 (1987) 225–253.CrossRefGoogle Scholar
[4]Burton, G. R., “Steady symmetric vortex pairs and rearrangements”, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988) 269–290.CrossRefGoogle Scholar
[5]Burton, G. R. and Emamizadeh, B., “A constrained variational problem for steady vortices in a shear flow”, Comm. Partial Differential Equations 24 (1999) 1341–1365.CrossRefGoogle Scholar
[6]Emamizadeh, B., “Steady vortex in a uniform shear flow of an ideal fluid”, Proc. Roy. Soc. Edinburgh Sect. A 130 (2000) 801–812.CrossRefGoogle Scholar
[7]Emamizadeh, B., “Existence of a steady flow with a bounded vortex in an unbounded domain”, J. Sciences I. Repub. Iran 12 (2001) 57–61.Google Scholar
[8]Emamizadeh, B. and Bahrami, F., “Steady vortex flows obtained from an inverse problem”, Bull. Austral. Math. Soc. 66 (2002) 213–226.CrossRefGoogle Scholar
[9]Emamizadeh, B. and Mehrabi, M. H., “Steady vortex flows obtained from a constrained variational problem”, Int. J. Math. Math. Sci. 30 (2002) 283–300.CrossRefGoogle Scholar
[10]Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order, 2nd ed. (Springer, Berlin, 1992).Google Scholar
[11]Grisvard, P., Singularities in boundary value problems (Masson, Springer, 1992).Google Scholar
[12]Marchioro, C. and Pulvirenti, M., Mathematical theory of incompressible nonviscous fluids (Springer, New York, 1994).CrossRefGoogle Scholar
[13]Turkington, B., “On steady vortex flow in two dimensions, I”, Comm. Partial Differential Equations 8 (1983) 999–1030.CrossRefGoogle Scholar
[14]Turkington, B., “On steady vortex flow in two dimensions, II”, Comm. Partial Differential Equations 8 (1983) 1031–1071.CrossRefGoogle Scholar