Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem

We consider the Taylor-Couette problem in an infinitely extended cylindrical domain. There exist modulated front solutions which describe the spreading of the stable Taylor vortices into the region of the unstable Couette flow. These transient solutions have the form of a front-like envelope advancing in the laboratory frame and leaving behind the stationary, spatially periodic Taylor vortices. We prove the nonlinear stability of these solutions with respect to small spatially localized perturbations.