# Non uniform Rotating Vortices and Periodic Orbits for the Two-Dimensional Euler Equations

@article{Garcia2020NonUR,
title={Non uniform Rotating Vortices and Periodic Orbits for the Two-Dimensional Euler Equations},
author={Claudia Garc'ia and Taoufik Hmidi and Juan Soler},
journal={Archive for Rational Mechanics and Analysis},
year={2020}
}
• Published 26 July 2018
• Mathematics
• Archive for Rational Mechanics and Analysis
This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different $m$--fold symmetries, $m\ge 1$. In particular, a complete study is provided for the truncated quadratic density $(A|x|^2+B){\bf{1}}_{\mathbb{D}}(x)$, with $\mathbb{D}$ the unit disc. We exhibit different behaviors with respect to the…
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