  The three-dimensional, homogeneous, incompressible Navier-Stokes equations
are studied in the absence of viscosity in one direction. It is shown that
there are arbitrarily large initial data generating a unique global solution,
the main feature of which is that they are slowly varying in the direction
where viscosity is missing. The difficulty arises from the complete absence of
a regularising effect in this direction. The special structure of the nonlinear
term, joint with the divergence-free condition on the velocity field, is
crucial in obtaining the result.
