Methods of centre manifold and multiple scales in the theory of weakly nonlinear stability for fluid motions

Abstract

The equivalence between the method of centre manifold and the method of multiple scales was examined when they are applied to the weakly nonlinear stability analysis for fluid motions. The relationship between the Landau equations of the seventh order, which were reduced from the Navier-Stokes equations by applying these two methods, is clarified. How we should define the disturbance amplitude to obtain the complete equivalence between them is discussed.