EXISTENCE OF SMALL LOOPS IN A BIFURCATION DIAGRAM NEAR THE DEGENERATE EIGENVALUES

Taoufik Hmidi (1) , Coralie Renault (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we study for the incompressible Euler equations the global structure of the bifurcation diagram for the rotating doubly connected patches near the degenerate case. We show that the branches with the same symmetry merge forming a small loop provided that they are close enough. This confirms the numerical observations done in the recent work [10].

Mots clés: Euler equations; Relative equilibria; Bifurcation diagram

Domaines: Equations aux dérivées partielles [math.AP]

Taoufik Hmidi, Coralie Renault. EXISTENCE OF SMALL LOOPS IN A BIFURCATION DIAGRAM NEAR THE DEGENERATE EIGENVALUES. Nonlinearity, 2017, 30 (10), pp.3821-3852. ⟨10.1088/1361-6544/aa82ef⟩. ⟨hal-01365301⟩