• DOI:10.1007/s00205-020-01561-z
• Corpus ID: 119593106

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

@article{Garcia2018NonUR,
  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={arXiv: Analysis of PDEs},
  year={2018}
}

• C. Garc'ia, Taoufik Hmidi, J. Soler
• Published 26 July 2018
• Mathematics
• arXiv: Analysis of PDEs

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.