A Hopf-bifurcation theorem for the critically dissipative quasi-geostrophic equation

TL;DR

This paper proves a Hopf-bifurcation theorem for the critically dissipative quasi-geostrophic equation on the torus, demonstrating the existence of time-dependent periodic solutions bifurcating from steady states.

Contribution

It establishes a Hopf-bifurcation result for the critically dissipative quasi-geostrophic equation, advancing understanding of its dynamical behavior.

Findings

Existence of time-dependent periodic solutions

Bifurcation from smooth steady solutions

Hopf-bifurcation theorem proven

Abstract

This paper is devoted to the study of the dynamical behavior of the critically dissipative quasi-geostrophic equation in $\textbf{T}^2$. We prove that this system possesses time-dependent periodic solutions, bifurcating from a smooth steady solution, i.e. a Hopf-Bifurcation theorem.