Global well-posedness of the two-dimensional exterior Navier-Stokes   equations for non-decaying data
  We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions for asymptotically constant initial data and arbitrary large Reynolds numbers. 
Ken Abe
math.AP