  We consider the incompressible and stationary Stokes equations on an infinite
two-dimensional wedge with non-scaling invariant Navier-slip boundary
conditions. We prove well-posedness and higher regularity of the Stokes problem
in a certain class of weighted Sobolev spaces.
  The novelty of this work is the occurrence of two different scalings in the
boundary condition, which is not treated so far for the Stokes system in
unbounded wedge-type domains. These difficulties are overcome by first
constructing a variational solution in a second order weighted Sobolev space
and subsequently proving higher regularity up to the tip of the wedge by
employing an iterative scheme. We believe that this method can be used for
other problems with variational structure and multiple scales.
