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arXiv · 1908.11093

Rotating vortex patches for the planar Euler equations in a disk

Daomin Cao·Jie Wan·Guodong Wang·Weicheng Zhan
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Abstract

We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limit of these rotating vortex patches is a rotating point vortex whose motion is described by the Kirchhoff-Routh equation. The construction is performed by solving a variational problem for the vorticity which is based on an adaption of Arnold's variational principle. We also prove nonlinear orbital stability of the set of maximizers in the variational problem under $L^p$ perturbation when $p\in[{3}/{2},+\infty)$.

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Daomin Cao, Jie Wan, Guodong Wang, Weicheng Zhan. 2019-08-29. Rotating vortex patches for the planar Euler equations in a disk. https://arxiv.org/abs/1908.11093

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