Doubly connected V-states for the generalized surface quasi-geostrophic equations

Abstract

In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with $\alpha\in ]0,1[.$ They can be described by countable branches bifurcating from the annulus at some explicit "eigenvalues" related to Bessel functions of the first kind. Contrary to Euler equations \cite{H-F-M-V}, we find V-states rotating with positive and negative angular velocities. At the end of the paper we discuss some numerical experiments concerning the limiting V-states.