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arXiv · 1807.02993

Existence of steady symmetric vortex patch in a disk

Daomin Cao·Guodong Wang·Bijun Zuo
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Abstract

In this paper we construct a family of steady symmetric vortex patches for the incompressible Euler equations in an open disk. The result is obtained by studying a variational problem in which the kinetic energy of the fluid is maximized subject to some appropriate constraints for the vorticity. Moreover, we show that these vortex patches shrink to a given minimum point of the corresponding Kirchhoff-Routh function as the vorticity strength parameter goes to infinity.

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Daomin Cao, Guodong Wang, Bijun Zuo. 2018-07-09. Existence of steady symmetric vortex patch in a disk. https://arxiv.org/abs/1807.02993

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