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

TL;DR

This paper proves the existence of convex global rotating solutions for the generalized surface quasi-geostrophic equations with certain parameters and establishes their boundary smoothness, advancing understanding of these fluid dynamics models.

Contribution

It confirms the existence of convex rotating solutions for a range of parameters and proves their boundary is infinitely smooth, filling gaps in previous research.

Findings

Existence of convex global rotating solutions for α in [1,2)

Boundary of solutions is infinitely smooth for α in (0,2)

Addresses open question from prior work on 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 $\alpha \in [1,2)$. We also show $C^{\infty}$ regularity of their boundary for all $\alpha \in (0,2)$.