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

2012/05/17 by Weiping Yan, Yong Li, Yan, Weiping +1
Engineering · Mathematics · #34C25 #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1205.3851

openalex publication_date 2012/05/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the study of the dynamical behavior of the critically dissipative quasi-geostrophic equation in T². We prove that this system possesses time-dependent periodic solutions, bifurcating from a smooth steady solution, i.e. a Hopf-Bifurcation theorem.

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