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

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 $(A|x{|}^2+B)1_{\mathbb{D}}(x)$, with $\mathbb{D}$ the unit disc. We exhibit different behaviors with respect to the coefficients $A$ and $B$ describing the rarefaction of bifurcating curves.

arXiv comment115 pages, 1 figure

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Cited by in corpus (4)

• Symmetry in stationary and uniformly-rotating solutions of active scalar equations
• Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
• Existence of corotating asymmetric vortex pairs for Euler equations
• Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations