On the asymptotic stability of steady solutions of the Navier-Stokes equations in unbounded domains

We consider the problem of the asymptotic behaviour in the L2-norm of solutions of the Navier-Stokes equations. We consider perturbations to the rest state and to stationary motions. In both cases we study the initial-boundary value problem in unbounded domains with non-compact boundary. In particular, we deal with domains with varying and possibly divergent exits to infinity and aperture domains.