Relative equilibria with holes for the surface quasi-geostrophic equations

TL;DR

This paper investigates the existence and regularity of doubly connected rotating patch solutions for the inviscid surface quasi-geostrophic equations, establishing their analyticity near the annulus configuration.

Contribution

It demonstrates the existence of doubly connected rotating patches and proves boundary analyticity near the annulus, extending previous open problems.

Findings

Existence of doubly connected rotating patches.

Boundaries are analytic curves near the annulus.

Addresses an open problem in the field.

Abstract

We study the existence of doubly connected rotating patches for the inviscid surface quasi- geostrophic equation left open in \cite{HHH}. By using the approach proposed by \cite{CCGS} we also prove that close to the annulus the boundaries are actually analytic curves.