Bifurcation of periodic solutions of the Navier-Stokes equations in a thin domain

Abstract

Aim of this paper is to provide conditions in order to guarantee that the periodic solutions in time and in the space variables of the Navier-Stokes equations bifurcate. Specifically, we study this problem when the considered state domain has one dimension which is small with respect to the others which we let to tend to zero. The thinness of the domain represents the bifurcation parameter in our situation.