  In [Lacave, IHP, ana, to appear (2008)] the author considered the two
dimensional Euler equations in the exterior of a thin obstacle shrinking to a
curve and determined the limit velocity. In the present work, we consider the
same problem in the viscous case, proving convergence to a solution of the
Navier-Stokes equations in the exterior of a curve. The uniqueness of the limit
solution is also shown.
