  Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi -
On the {V}-states for the generalized quasi-geostrophic equations,arXiv
preprint arXiv:1405.0858], we close the question of the existence of convex
global rotating solutions for the generalized surface quasi-geostrophic
equation for $\alpha \in [1,2)$. We also show $C^{\infty}$ regularity of their
boundary for all $\alpha \in (0,2)$.
