The existence theorem for the steady Navier--Stokes problem in exterior   axially symmetric 3D domains
  We study the nonhomogeneous boundary value problem for the Navier--Stokes equations of steady motion of a viscous incompressible fluid in a three--dimensional exterior domain with multiply connected boundary. We prove that this problem has a solution for axially symmetric domains and data (without any smallness restrictions on the fluxes). 
Mikhail Korobkov, Konstantin Pileckas, Remigio Russo
math.AP