On the Asymptotic Stability of Steady Flows with Nonzero Flux in Two-Dimensional Exterior Domains

The Navier–Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any L 2 -perturbation. In particular, the general hypothesis is valid if the steady solution is the sum of the critically decaying flux carrier with flux Φ < 2 π and a small subcritically decaying term. Under the central symmetry assumption, the general hypothesis is also proven for any critically decaying steady solutions under a suitable smallness condition.