The relation between stationary and periodic solutions of the Navier-Stokes equations in two or three dimensional channels

Abstract

In this paper we will consider whether there exists a time periodic solution of the Navier-Stokes equations for infinite channels in $\mathbb{R}^n(n=2,3)$. H. Beirão da Veiga [4] treated such a problem. This paper is the special case of his paper and we argue the relation between the existence of stationary and time periodic solutions of the Navier-Stokes equations.