A finite time result for vanishing viscosity in the plane with   nondecaying vorticity
  Assuming that initial velocity has finite energy and initial vorticity is bounded in the plane, we show that for any finite time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the Euler equations as viscosity approaches zero. We also establish a rate of convergence. 
Elaine Cozzi