Existence and exponential stability in Lr-spaces of stationary Navier-Stokes flows with prescribed flux in infinite cylindrical domains

We prove existence, uniqueness and exponential stability of stationary Navier-Stokes flows with prescribed flux in an unbounded cylinder of Rn,n>3, with several exits to infinity provided the total flux and external force are sufficiently small. The proofs are based on analytic semigroup theory, perturbation theory and Lr - Lq-estimates of a perturbation of the Stokes operator in Lq-spaces.