  We study the generalized stationary Stokes system in a bounded domain in the
plane equipped with perfect slip boundary conditions. We show natural stability
results in oscillatory spaces, i.e. H\"older spaces and Campanato spaces
including the border-line spaces of bounded mean oscillations (BMO) and
vanishing mean oscillations (VMO). In particular, we show that under
appropriate assumptions gradients of solutions are globally continuous. Since
the stress tensor is assumed to be governed by a general Orlicz function, our
theory includes various cases of (possibly degenerate) shear thickening and
shear thinning fluids; including the model case of power law fluids. The global
estimates seem to be new even in case of the linear Stokes system.
