Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations

Abstract

Motivated by the recent work of Hassainia and Hmidi, 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 $\alpha \in (0,2)$.