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arXiv · 1909.00359

On radial symmetry of rotating vortex patches in the disc

Guodong Wang·Bijun Zuo
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Abstract

In this note, we consider the radial symmetry property of rotating vortex patches for the 2D incompressible Euler equations in the unit disc. By choosing a suitable vector field to deform the patch, we show that each simply-connected rotating vortex patch $D$ with angular velocity $\Omega$, $\Omega\geq \max\{{1}/{2},({2 l^2})/{(1-l^2)^2}\}$ or $\Omega\leq -({2 l^2})/{(1-l^2)^2}$, where $l=\sup_{x\in D}|x|$, must be a disc. The main idea of the proof, which has a variational flavor, comes from a very recent paper of G\'omez-Serrano--Park--Shi--Yao, arXiv:1908.01722, where radial symmetry of rotating vortex patches in the whole plane was studied.

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Guodong Wang, Bijun Zuo. 2019-09-01. On radial symmetry of rotating vortex patches in the disc. https://arxiv.org/abs/1909.00359

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