Rearrangements in steady vortex flows with circulation

Elcrat, Alan R.; Miller, Kenneth G.

doi:10.1090/S0002-9939-1991-1043409-2

Rearrangements in steady vortex flows with circulation
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by Alan R. Elcrat and Kenneth G. Miller

Proc. Amer. Math. Soc. 111 (1991), 1051-1055

DOI: https://doi.org/10.1090/S0002-9939-1991-1043409-2

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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.

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On steady vortex flows in two dimensions

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