Multi-pulse solutions to the Navier-Stokes problem between parallel plates

We consider the three-dimensional Poiseuille problem of a viscous incompres sible fluid how between parallel plates. The flows under investigation are assumed to be traveling waves in streamwise direction with spatial periodic ity 2 pi/alpha(. In spanwise direction they are assumed to be uniformly clo se to the basic flow which enables us to use the spatial center-manifold re duction, where the spanwise variable takes the role of the time. For Reynol ds numbers close to criticality the problem is reduced to a four-dimensiona l ODE whose lowest order terms coincide with the steady complex Ginzburg-La ndau equation. Using perturbation arguments we relate reversible n-pulse so lutions of this equation to n-pulse solutions of the problem on a center ma nifold. Thus, we obtain multi-pulse solutions of the Navier-Stokes problem for parameters slightly below criticality. These solutions are localized in spanwise direction but periodic in streamwise direction.