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December  2004, 3(4): 663-674. doi: 10.3934/cpaa.2004.3.663

Steiner symmetric vortices attached to seamounts

B. Emamizadeh 1, , F. Bahrami 2, and  M. H. Mehrabi 3,

1. 

Institute for Studies in Theoretical Physics and Mathematics, Niavaran square, Tehran, Iran
2. 

Department of Mathematics, Tarbiat Modares University, P.O. Box 14155-4838, Tehran, Iran
3. 

Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

Received  November 2003 Revised  June 2004 Published  September 2004

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.
Keywords: variational prob- lems, vortices, Barotropic vorticity equation, Steiner symmetrization, Rearrangements, semilinear elliptic equation.
Mathematics Subject Classification: 35J60, 76B03, 76B47, 76M30, 76U0.
Citation: B. Emamizadeh, F. Bahrami, M. H. Mehrabi. Steiner symmetric vortices attached to seamounts. Communications on Pure & Applied Analysis, 2004, 3 (4) : 663-674. doi: 10.3934/cpaa.2004.3.663
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