Bifurcating fronts for the Taylor-Couette problem in infinite cylinders

We show the existence of bifurcating fronts for the weakly unstable Taylor- Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground stat e, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcatin g fronts for the Swift-Hohenberg equation by Collet & Eckmann, 1986, and by Eckmann & Wayne, 1991. The existence proof is based on spatial dynamics an d center manifold theory. One of the difficulties in applying center manifo ld theory comes from an infinite number of eigenvalues on the imaginary axi s for vanishing bifurcation parameter. But nevertheless, a finite dimension al reduction is possible, since the eigenvalues leave the imaginary axis wi th different velocities, if the bifurcation parameter is increased. In cont rast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to conta in the bifurcating fronts.