Ken Abe

We consider the two-dimensional Navies-Stokes equations in an exterior domain, subject to the Dirichlet boundary condition. Stationary solutions of this problem and their asymptotic behavior
have been studied in a large literature, while a few results are known about the non-stationary problem for non-decaying initial data. We report some global well-posedness result for bounded initial data
with a finite Dirichlet integral, and unique existence of asymptotically constant solutions for arbitrary large Reynolds numbers.