Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations

Claudia García; Taoufik Hmidi; Juan Soler

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arXiv · 1807.10017

Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations

Claudia García·Taoufik Hmidi·Juan Soler

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Abstract

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 coefficients $A$ and $B$ describing the rarefaction of bifurcating curves.

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Claudia García, Taoufik Hmidi, Juan Soler. 2018-07-26. Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations. https://arxiv.org/abs/1807.10017

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