  We study a generalized Stokes system with Orlicz growth which is nonstandard
in a non-smooth domain. Our purpose is to derive a Calderon-Zygmund type
estimate of the gradient of a solution and the pressure to such a system like
(1.1) under a small BMO non-linearity and a sufficient flatness on the boundary
of the domain. In the process, we overcome not only lack of Lipschitz
regularity for the corresponding limiting problem, but also the fact that the
associated structure depends only on the symmetric part of the gradient for the
desired global estimate, which is new even in the literature of elliptic system
on a nonsmooth domain.
