Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

Yiming Long, Yuchen Wang, Chongchun Zeng

We consider concentrated vorticities for the Euler equation on a smooth domain $\Omega \subset {\mathbf{R}}^2$ in the form of \[ ω= \sum_{j=1}^N ω_j χ_{Ω_j}, \quad |Ω_j| = πr_j^2, \quad \i…