The existence theorem for steady Navier--Stokes equations in the axially   symmetric case
  We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded multiply connected domain. We prove that this problem has a solution in some axially symmetric cases, in particular, when all components of the boundary intersect the axis of symmetry. 
Mikhail Korobkov, Konstantin Pileckas, Remigio Russo
math-ph math.MP