On the V-states for the generalized quasi-geostrophic equations

TL;DR

This paper proves the existence of rotating V-states with specific symmetries for the generalized inviscid SQG equations, revealing an infinite family of non-stationary solutions with uniqueness.

Contribution

It establishes the existence of V-states for the generalized SQG equations with lpha in (0,1), including explicit bifurcation points and an infinite family of solutions.

Findings

Existence of V-states for lpha in (0,1)

Bifurcation from trivial solutions at explicit angular velocities

Infinite family of non-stationary, globally defined solutions

Abstract

We prove the existence of the V-states for the generalized inviscid SQG equations with $\alpha\in ]0,1[.$ These structures are special rotating simply connected patches with $m-$ fold symmetry bifurcating from the trivial solution at some explicit values of the angular velocity. This produces, inter alia, an infinite family of non stationary global solutions with uniqueness.