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

Abstract

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 $\hat{I}\pm \in [1,2)$. We also show $C^{\infty }$ regularity of their boundary for all $\hat{I}\pm \in (0,2)$.

42 pages