A Hopf-Bifurcation Theorem for the Vorticity Formulation of the Navier–Stokes Equations in ℝ³

Abstract

We prove a Hopf-bifurcation theorem for the vorticity formulation of the Navier–Stokes equations in ℝ3 in case of spatially localized external forcing. The difficulties are due to essential spectrum up to the imaginary axis for all values of the bifurcation parameter which a priori no longer allows to reduce the problem to a finite dimensional one.