Steiner symmetric vortices attached to seamounts

B. Emamizadeh; F. Bahrami; M. H. Mehrabi

doi:10.3934/cpaa.2004.3.663

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2004, Volume 3, Issue 4: 663-674. Doi: 10.3934/cpaa.2004.3.663

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Steiner symmetric vortices attached to seamounts

1.
Institute for Studies in Theoretical Physics and Mathematics, Niavaran square, Tehran
2.
Department of Mathematics, Tarbiat Modares University, P.O. Box 14155-4838, Tehran
3.
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran

Received: October 31, 2003

Revised: May 31, 2004

Published: November 2004

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Abstract

We prove existence of Steiner symmetric maximizers for a constrained variational problem in $\mathbb R^2$. Solutions represent steady geophysical flows over a surface of variable height. The kinetic energy is maximized with respect to the set formed by intersecting a set of rearrangements of a given function with an affine subspace of codimension one.

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Mathematics Subject Classification: 35J60, 76B03, 76B47, 76M30, 76U05.

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